616:
384:
1203:
1015:
741:
853:
611:{\displaystyle \dots \to H^{1}(\mathbb {C} ^{n},{\underline {\mathbb {Z} }})\to H^{1}(\mathbb {C} ^{n},{\mathcal {O}}_{\mathbb {C} ^{n}})\to H^{1}(\mathbb {C} ^{n},{\mathcal {O}}_{\mathbb {C} ^{n}}^{\star })\to H^{2}(\mathbb {C} ^{n},{\underline {\mathbb {Z} }})\to \cdots }
1024:
1655:
1444:
887:
627:
746:
373:
162:
1771:
1198:{\displaystyle H^{1}(\mathbb {C} ^{n},{\mathcal {O}}_{\mathbb {C} ^{n}})\simeq H^{1}(\mathbb {C} ^{n},\Omega _{\mathbb {C} ^{n}}^{0})\simeq H_{\bar {\partial }}^{0,1}(\mathbb {C} ^{n})=0}
276:
1547:
1704:
882:
1813:
1349:
322:
1010:{\displaystyle H^{1}(\mathbb {C} ^{n},{\mathcal {O}}_{\mathbb {C} ^{n}})\simeq H^{1}(\mathbb {C} ^{n},{\mathcal {O}}_{\mathbb {C} ^{n}}^{\star })}
736:{\displaystyle H^{k}(\mathbb {C} ^{n},{\underline {\mathbb {Z} }})\simeq H_{\scriptscriptstyle {\rm {sing}}}^{k}(\mathbb {C} ^{n};\mathbb {Z} )}
2156:
2115:
1982:
1227:
848:{\displaystyle H^{1}(\mathbb {C} ^{n},{\underline {\mathbb {Z} }})\simeq H^{2}(\mathbb {C} ^{n},{\underline {\mathbb {Z} }})\simeq 0}
1323:
331:
1490:
2182:
2066:
1482:
105:
2192:
2107:
1729:
176:
1332:
1968:
1260:
2148:
1869:
1650:{\displaystyle \operatorname {Pic} _{X/S}(T)=\operatorname {Pic} (X_{T})/f_{T}^{*}(\operatorname {Pic} (T))}
2187:
1950:
1936:
1493:, the classification becomes amenable to discrete invariants. Algebraic equivalence is closely related to
244:
1494:
1478:
1219:
1663:
858:
2080:
2019:
1889:
1879:
1206:
1018:
376:
325:
168:
31:
1522:
1498:
1256:
239:
232:
1959:, Séminaire Bourbaki, t. 14: année 1961/62, exposés 223-240, no. 7, Talk no. 236, pp. 221–243
1945:, Séminaire Bourbaki, t. 14: année 1961/62, exposés 223-240, no. 7, Talk no. 232, pp. 143–161
2070:
200:
85:
61:
2162:
2152:
2129:
2111:
2047:
1996:
1978:
1874:
209:
187:
81:
2037:
2027:
1964:
1908:
1854:
1788:
1454:
1288:
1280:
1249:
217:
96:
89:
2125:
2092:
1992:
1439:{\displaystyle 1\to \mathrm {Pic} ^{0}(V)\to \mathrm {Pic} (V)\to \mathrm {NS} (V)\to 1.\,}
80:. This construction is a global version of the construction of the divisor class group, or
2121:
2088:
1988:
1974:
1864:
1308:
1268:
1264:
1246:
204:
172:
73:
183:
2084:
2023:
2058:
2007:
1954:
1940:
1341:
1296:
307:
236:
77:
2042:
27:
Mathematical group occurring in algebraic geometry and the theory of complex manifolds
2176:
2140:
2099:
1859:
46:
1884:
65:
57:
38:
2133:
17:
2000:
2051:
2032:
2166:
1489:; that is, using a stronger, non-linear equivalence relation in place of
1245:
In the cases of most importance to classical algebraic geometry, for a
2075:
1226:, is an important step in algebraic geometry, in particular in the
1287:
is a curve, the Picard variety is naturally isomorphic to the
1909:
Sheaf cohomology#Sheaf cohomology with constant coefficients
1059:
979:
922:
528:
471:
250:
131:
2010:(1955), "On some problems in abstract algebraic geometry",
2065:, Math. Surveys Monogr., vol. 123, Providence, R.I.:
293:
The Picard group of the affine line with two origins over
368:{\displaystyle \operatorname {Pic} (\mathbb {C} ^{n})=0}
379:
yields the following long exact sequence in cohomology
1299:
constructed an example of a smooth projective surface
682:
95:
Alternatively, the Picard group can be defined as the
1791:
1732:
1666:
1550:
1352:
1027:
890:
861:
749:
630:
387:
334:
310:
247:
171:
the Picard group is isomorphic to the class group of
108:
1836:(when the degree is defined for the Picard group of
1295:. For fields of positive characteristic however,
1807:
1765:
1698:
1649:
1438:
1197:
1009:
876:
847:
735:
610:
367:
316:
270:
157:{\displaystyle H^{1}(X,{\mathcal {O}}_{X}^{*}).\,}
156:
1340:. In other words, the Picard group fits into an
2106:, Annals of Mathematics Studies, vol. 59,
1956:VI. Les schémas de Picard. Propriétés générales
1942:V. Les schémas de Picard. Théorèmes d'existence
1497:, an essentially topological classification by
1766:{\displaystyle \operatorname {Pic} _{X/S}(T)}
179:gives basic information on the Picard group.
8:
1231:
1279:). The dual of the Picard variety is the
1267:of the identity in the Picard scheme is an
1218:The construction of a scheme structure on (
2104:Lectures on Curves on an Algebraic Surface
186:'s theories, in particular of divisors on
2074:
2041:
2031:
1796:
1790:
1741:
1737:
1731:
1684:
1671:
1665:
1620:
1615:
1606:
1597:
1559:
1555:
1549:
1435:
1412:
1389:
1371:
1360:
1351:
1180:
1176:
1175:
1159:
1148:
1147:
1131:
1124:
1120:
1119:
1117:
1104:
1100:
1099:
1089:
1071:
1067:
1066:
1064:
1058:
1057:
1047:
1043:
1042:
1032:
1026:
998:
991:
987:
986:
984:
978:
977:
967:
963:
962:
952:
934:
930:
929:
927:
921:
920:
910:
906:
905:
895:
889:
868:
864:
863:
860:
827:
826:
824:
815:
811:
810:
800:
781:
780:
778:
769:
765:
764:
754:
748:
726:
725:
716:
712:
711:
701:
684:
683:
681:
662:
661:
659:
650:
646:
645:
635:
629:
590:
589:
587:
578:
574:
573:
563:
547:
540:
536:
535:
533:
527:
526:
516:
512:
511:
501:
483:
479:
478:
476:
470:
469:
459:
455:
454:
444:
425:
424:
422:
413:
409:
408:
398:
386:
350:
346:
345:
333:
309:
267:
249:
248:
246:
153:
141:
136:
130:
129:
113:
107:
1533:if it is a scheme) is given by: for any
1919:
1901:
1239:
1235:
1827:as an invertible sheaf over the fiber
7:
271:{\displaystyle {\mathcal {O}}(m),\,}
1283:, and in the particular case where
1228:duality theory of abelian varieties
1416:
1413:
1396:
1393:
1390:
1367:
1364:
1361:
1222:version of) the Picard group, the
1150:
1114:
694:
691:
688:
685:
25:
1699:{\displaystyle f_{T}:X_{T}\to T}
1324:finitely-generated abelian group
1307:) non-reduced, and hence not an
877:{\displaystyle \mathbb {C} ^{n}}
2063:Fundamental algebraic geometry
1760:
1754:
1690:
1644:
1641:
1635:
1626:
1603:
1590:
1578:
1572:
1491:linear equivalence of divisors
1429:
1426:
1420:
1409:
1406:
1400:
1386:
1383:
1377:
1356:
1186:
1171:
1153:
1137:
1095:
1079:
1038:
1004:
958:
942:
901:
836:
806:
790:
760:
730:
707:
671:
641:
602:
599:
569:
556:
553:
507:
494:
491:
450:
437:
434:
404:
391:
356:
341:
261:
255:
147:
119:
1:
2067:American Mathematical Society
2061:(2005), "The Picard scheme",
2012:Proc. Natl. Acad. Sci. U.S.A.
1449:The fact that the rank of NS(
1207:Dolbeault–Grothendieck lemma
175:. For complex manifolds the
1777:if for any geometric point
2209:
2108:Princeton University Press
216:The invertible sheaves on
177:exponential sheaf sequence
29:
182:The name is in honour of
1333:NĂ©ron–Severi group
1234:, and also described by
1230:. It was constructed by
304:The Picard group of the
199:The Picard group of the
30:Not to be confused with
2149:Oxford University Press
1870:Holomorphic line bundle
1527:relative Picard functor
1469:, often denoted ρ(
278:so the Picard group of
2033:10.1073/pnas.41.11.964
1809:
1808:{\displaystyle s^{*}L}
1767:
1706:is the base change of
1700:
1651:
1531:relative Picard scheme
1505:Relative Picard scheme
1440:
1199:
1011:
884:is contractible, then
878:
849:
737:
612:
369:
318:
272:
158:
84:, and is much used in
1810:
1768:
1701:
1652:
1495:numerical equivalence
1479:algebraic equivalence
1441:
1220:representable functor
1200:
1019:Dolbeault isomorphism
1017:and we can apply the
1012:
879:
850:
738:
613:
370:
319:
273:
159:
2183:Geometry of divisors
2069:, pp. 235–321,
1973:, Berlin, New York:
1880:Arakelov class group
1789:
1730:
1664:
1548:
1499:intersection numbers
1473:). Geometrically NS(
1350:
1025:
888:
859:
747:
628:
385:
377:exponential sequence
332:
326:complex affine space
308:
245:
106:
32:Picard modular group
2085:2005math......4020K
2024:1955PNAS...41..964I
1922:, Definition 9.2.2.
1625:
1523:morphism of schemes
1459:theorem of the base
1265:connected component
1232:Grothendieck (1962)
1170:
1136:
1003:
706:
552:
286:) is isomorphic to
146:
56:), is the group of
2059:Kleiman, Steven L.
1970:Algebraic Geometry
1805:
1763:
1696:
1647:
1611:
1461:; the rank is the
1436:
1195:
1143:
1113:
1007:
976:
874:
845:
834:
788:
733:
699:
677:
669:
608:
597:
525:
432:
365:
314:
268:
188:algebraic surfaces
154:
128:
88:and the theory of
86:algebraic geometry
62:invertible sheaves
2193:Abelian varieties
2158:978-0-19-560528-0
2145:Abelian varieties
2117:978-0-691-07993-6
1984:978-0-387-90244-9
1965:Hartshorne, Robin
1875:Ideal class group
1719:is the pullback.
1314:The quotient Pic(
1156:
825:
779:
660:
588:
423:
317:{\displaystyle n}
297:is isomorphic to
210:ideal class group
90:complex manifolds
82:ideal class group
52:, denoted by Pic(
16:(Redirected from
2200:
2169:
2136:
2095:
2078:
2054:
2045:
2035:
2003:
1960:
1951:Grothendieck, A.
1946:
1937:Grothendieck, A.
1923:
1917:
1911:
1906:
1855:Sheaf cohomology
1814:
1812:
1811:
1806:
1801:
1800:
1772:
1770:
1769:
1764:
1750:
1749:
1745:
1705:
1703:
1702:
1697:
1689:
1688:
1676:
1675:
1656:
1654:
1653:
1648:
1624:
1619:
1610:
1602:
1601:
1568:
1567:
1563:
1477:) describes the
1455:Francesco Severi
1445:
1443:
1442:
1437:
1419:
1399:
1376:
1375:
1370:
1289:Jacobian variety
1281:Albanese variety
1275:and denoted Pic(
1250:complete variety
1204:
1202:
1201:
1196:
1185:
1184:
1179:
1169:
1158:
1157:
1149:
1135:
1130:
1129:
1128:
1123:
1109:
1108:
1103:
1094:
1093:
1078:
1077:
1076:
1075:
1070:
1063:
1062:
1052:
1051:
1046:
1037:
1036:
1016:
1014:
1013:
1008:
1002:
997:
996:
995:
990:
983:
982:
972:
971:
966:
957:
956:
941:
940:
939:
938:
933:
926:
925:
915:
914:
909:
900:
899:
883:
881:
880:
875:
873:
872:
867:
854:
852:
851:
846:
835:
830:
820:
819:
814:
805:
804:
789:
784:
774:
773:
768:
759:
758:
742:
740:
739:
734:
729:
721:
720:
715:
705:
700:
698:
697:
670:
665:
655:
654:
649:
640:
639:
617:
615:
614:
609:
598:
593:
583:
582:
577:
568:
567:
551:
546:
545:
544:
539:
532:
531:
521:
520:
515:
506:
505:
490:
489:
488:
487:
482:
475:
474:
464:
463:
458:
449:
448:
433:
428:
418:
417:
412:
403:
402:
374:
372:
371:
366:
355:
354:
349:
323:
321:
320:
315:
277:
275:
274:
269:
254:
253:
218:projective space
173:Cartier divisors
163:
161:
160:
155:
145:
140:
135:
134:
118:
117:
97:sheaf cohomology
21:
2208:
2207:
2203:
2202:
2201:
2199:
2198:
2197:
2173:
2172:
2159:
2139:
2118:
2098:
2057:
2018:(11): 964–967,
2008:Igusa, Jun-Ichi
2006:
1985:
1975:Springer-Verlag
1963:
1949:
1935:
1932:
1927:
1926:
1918:
1914:
1907:
1903:
1898:
1890:Picard category
1865:Cartier divisor
1851:
1844:
1835:
1792:
1787:
1786:
1733:
1728:
1727:
1718:
1680:
1667:
1662:
1661:
1593:
1551:
1546:
1545:
1507:
1453:) is finite is
1359:
1348:
1347:
1309:abelian variety
1269:abelian variety
1216:
1174:
1118:
1098:
1085:
1065:
1056:
1041:
1028:
1023:
1022:
985:
961:
948:
928:
919:
904:
891:
886:
885:
862:
857:
856:
809:
796:
763:
750:
745:
744:
710:
644:
631:
626:
625:
572:
559:
534:
510:
497:
477:
468:
453:
440:
407:
394:
383:
382:
344:
330:
329:
306:
305:
243:
242:
205:Dedekind domain
196:
109:
104:
103:
74:group operation
35:
28:
23:
22:
15:
12:
11:
5:
2206:
2204:
2196:
2195:
2190:
2185:
2175:
2174:
2171:
2170:
2157:
2141:Mumford, David
2137:
2116:
2100:Mumford, David
2096:
2055:
2004:
1983:
1961:
1947:
1931:
1928:
1925:
1924:
1912:
1900:
1899:
1897:
1894:
1893:
1892:
1887:
1882:
1877:
1872:
1867:
1862:
1857:
1850:
1847:
1840:
1831:
1804:
1799:
1795:
1762:
1759:
1756:
1753:
1748:
1744:
1740:
1736:
1714:
1695:
1692:
1687:
1683:
1679:
1674:
1670:
1658:
1657:
1646:
1643:
1640:
1637:
1634:
1631:
1628:
1623:
1618:
1614:
1609:
1605:
1600:
1596:
1592:
1589:
1586:
1583:
1580:
1577:
1574:
1571:
1566:
1562:
1558:
1554:
1506:
1503:
1447:
1446:
1434:
1431:
1428:
1425:
1422:
1418:
1415:
1411:
1408:
1405:
1402:
1398:
1395:
1392:
1388:
1385:
1382:
1379:
1374:
1369:
1366:
1363:
1358:
1355:
1342:exact sequence
1273:Picard variety
1261:characteristic
1240:Kleiman (2005)
1236:Mumford (1966)
1215:
1212:
1211:
1210:
1194:
1191:
1188:
1183:
1178:
1173:
1168:
1165:
1162:
1155:
1152:
1146:
1142:
1139:
1134:
1127:
1122:
1116:
1112:
1107:
1102:
1097:
1092:
1088:
1084:
1081:
1074:
1069:
1061:
1055:
1050:
1045:
1040:
1035:
1031:
1006:
1001:
994:
989:
981:
975:
970:
965:
960:
955:
951:
947:
944:
937:
932:
924:
918:
913:
908:
903:
898:
894:
871:
866:
844:
841:
838:
833:
829:
823:
818:
813:
808:
803:
799:
795:
792:
787:
783:
777:
772:
767:
762:
757:
753:
732:
728:
724:
719:
714:
709:
704:
696:
693:
690:
687:
680:
676:
673:
668:
664:
658:
653:
648:
643:
638:
634:
621:
620:
619:
618:
607:
604:
601:
596:
592:
586:
581:
576:
571:
566:
562:
558:
555:
550:
543:
538:
530:
524:
519:
514:
509:
504:
500:
496:
493:
486:
481:
473:
467:
462:
457:
452:
447:
443:
439:
436:
431:
427:
421:
416:
411:
406:
401:
397:
393:
390:
364:
361:
358:
353:
348:
343:
340:
337:
313:
302:
291:
266:
263:
260:
257:
252:
214:
195:
192:
165:
164:
152:
149:
144:
139:
133:
127:
124:
121:
116:
112:
78:tensor product
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2205:
2194:
2191:
2189:
2188:Scheme theory
2186:
2184:
2181:
2180:
2178:
2168:
2164:
2160:
2154:
2150:
2146:
2142:
2138:
2135:
2131:
2127:
2123:
2119:
2113:
2109:
2105:
2101:
2097:
2094:
2090:
2086:
2082:
2077:
2072:
2068:
2064:
2060:
2056:
2053:
2049:
2044:
2039:
2034:
2029:
2025:
2021:
2017:
2013:
2009:
2005:
2002:
1998:
1994:
1990:
1986:
1980:
1976:
1972:
1971:
1966:
1962:
1958:
1957:
1952:
1948:
1944:
1943:
1938:
1934:
1933:
1929:
1921:
1916:
1913:
1910:
1905:
1902:
1895:
1891:
1888:
1886:
1883:
1881:
1878:
1876:
1873:
1871:
1868:
1866:
1863:
1861:
1858:
1856:
1853:
1852:
1848:
1846:
1843:
1839:
1834:
1830:
1826:
1822:
1818:
1802:
1797:
1793:
1785:the pullback
1784:
1780:
1776:
1757:
1751:
1746:
1742:
1738:
1734:
1725:
1720:
1717:
1713:
1709:
1693:
1685:
1681:
1677:
1672:
1668:
1638:
1632:
1629:
1621:
1616:
1612:
1607:
1598:
1594:
1587:
1584:
1581:
1575:
1569:
1564:
1560:
1556:
1552:
1544:
1543:
1542:
1540:
1536:
1532:
1528:
1524:
1520:
1516:
1512:
1504:
1502:
1500:
1496:
1492:
1488:
1484:
1480:
1476:
1472:
1468:
1464:
1463:Picard number
1460:
1456:
1452:
1432:
1423:
1403:
1380:
1372:
1353:
1346:
1345:
1344:
1343:
1339:
1335:
1334:
1329:
1325:
1321:
1317:
1312:
1310:
1306:
1302:
1298:
1294:
1290:
1286:
1282:
1278:
1274:
1270:
1266:
1262:
1258:
1254:
1251:
1248:
1243:
1241:
1237:
1233:
1229:
1225:
1224:Picard scheme
1221:
1214:Picard scheme
1213:
1208:
1192:
1189:
1181:
1166:
1163:
1160:
1144:
1140:
1132:
1125:
1110:
1105:
1090:
1086:
1082:
1072:
1053:
1048:
1033:
1029:
1021:to calculate
1020:
999:
992:
973:
968:
953:
949:
945:
935:
916:
911:
896:
892:
869:
842:
839:
831:
821:
816:
801:
797:
793:
785:
775:
770:
755:
751:
722:
717:
702:
678:
674:
666:
656:
651:
636:
632:
623:
622:
605:
594:
584:
579:
564:
560:
548:
541:
522:
517:
502:
498:
484:
465:
460:
445:
441:
429:
419:
414:
399:
395:
388:
381:
380:
378:
375:, indeed the
362:
359:
351:
338:
335:
327:
324:-dimensional
311:
303:
300:
296:
292:
289:
285:
281:
264:
258:
241:
238:
234:
230:
226:
222:
219:
215:
212:
211:
206:
202:
198:
197:
193:
191:
189:
185:
180:
178:
174:
170:
167:For integral
150:
142:
137:
125:
122:
114:
110:
102:
101:
100:
98:
93:
91:
87:
83:
79:
75:
71:
67:
63:
59:
55:
51:
48:
44:
40:
33:
19:
18:Picard scheme
2144:
2103:
2076:math/0504020
2062:
2015:
2011:
1969:
1955:
1941:
1920:Kleiman 2005
1915:
1904:
1860:Chow variety
1841:
1837:
1832:
1828:
1824:
1820:
1816:
1782:
1778:
1774:
1723:
1721:
1715:
1711:
1707:
1659:
1538:
1534:
1530:
1526:
1518:
1514:
1510:
1508:
1486:
1474:
1470:
1466:
1462:
1458:
1450:
1448:
1337:
1331:
1327:
1319:
1315:
1313:
1304:
1300:
1292:
1284:
1276:
1272:
1252:
1247:non-singular
1244:
1223:
1217:
298:
294:
287:
283:
279:
228:
224:
220:
208:
184:Émile Picard
181:
166:
94:
69:
66:line bundles
53:
49:
47:ringed space
43:Picard group
42:
36:
1885:Group-stack
1823:has degree
1773:has degree
1481:classes of
1326:denoted NS(
1271:called the
72:, with the
60:classes of
58:isomorphism
39:mathematics
2177:Categories
2147:, Oxford:
1930:References
1722:We say an
1263:zero, the
624:and since
235:, are the
2134:171541070
1798:∗
1752:
1691:→
1633:
1622:∗
1588:
1570:
1430:→
1410:→
1387:→
1357:→
1303:with Pic(
1154:¯
1151:∂
1141:≃
1115:Ω
1083:≃
1000:⋆
946:≃
840:≃
832:_
794:≃
786:_
675:≃
667:_
606:⋯
603:→
595:_
557:→
549:⋆
495:→
438:→
430:_
392:→
389:⋯
339:
143:∗
2143:(1970),
2102:(1966),
2052:16589782
2001:13348052
1967:(1977),
1953:(1962),
1939:(1962),
1849:See also
1537:-scheme
1483:divisors
855:because
743:we have
237:twisting
201:spectrum
194:Examples
2126:0209285
2093:2223410
2081:Bibcode
2020:Bibcode
1993:0463157
1330:), the
1322:) is a
1255:over a
1205:by the
240:sheaves
207:is its
169:schemes
2167:138290
2165:
2155:
2132:
2124:
2114:
2091:
2050:
2043:534315
2040:
1999:
1991:
1981:
1819:along
1660:where
1525:. The
1318:)/Pic(
227:) for
99:group
76:being
41:, the
2071:arXiv
1896:Notes
1521:be a
1297:Igusa
1257:field
233:field
203:of a
68:) on
45:of a
2163:OCLC
2153:ISBN
2130:OCLC
2112:ISBN
2048:PMID
1997:OCLC
1979:ISBN
1710:and
1529:(or
1509:Let
1238:and
64:(or
2038:PMC
2028:doi
1845:.)
1815:of
1735:Pic
1726:in
1630:Pic
1585:Pic
1553:Pic
1485:on
1465:of
1457:'s
1336:of
1291:of
1259:of
336:Pic
37:In
2179::
2161:,
2151:,
2128:,
2122:MR
2120:,
2110:,
2089:MR
2087:,
2079:,
2046:,
2036:,
2026:,
2016:41
2014:,
1995:,
1989:MR
1987:,
1977:,
1781:→
1541:,
1513::
1501:.
1433:1.
1311:.
1242:.
328::
231:a
190:.
92:.
2083::
2073::
2030::
2022::
1842:s
1838:X
1833:s
1829:X
1825:r
1821:s
1817:L
1803:L
1794:s
1783:T
1779:s
1775:r
1761:)
1758:T
1755:(
1747:S
1743:/
1739:X
1724:L
1716:T
1712:f
1708:f
1694:T
1686:T
1682:X
1678::
1673:T
1669:f
1645:)
1642:)
1639:T
1636:(
1627:(
1617:T
1613:f
1608:/
1604:)
1599:T
1595:X
1591:(
1582:=
1579:)
1576:T
1573:(
1565:S
1561:/
1557:X
1539:T
1535:S
1519:S
1517:→
1515:X
1511:f
1487:V
1475:V
1471:V
1467:V
1451:V
1427:)
1424:V
1421:(
1417:S
1414:N
1407:)
1404:V
1401:(
1397:c
1394:i
1391:P
1384:)
1381:V
1378:(
1373:0
1368:c
1365:i
1362:P
1354:1
1338:V
1328:V
1320:V
1316:V
1305:S
1301:S
1293:V
1285:V
1277:V
1253:V
1209:.
1193:0
1190:=
1187:)
1182:n
1177:C
1172:(
1167:1
1164:,
1161:0
1145:H
1138:)
1133:0
1126:n
1121:C
1111:,
1106:n
1101:C
1096:(
1091:1
1087:H
1080:)
1073:n
1068:C
1060:O
1054:,
1049:n
1044:C
1039:(
1034:1
1030:H
1005:)
993:n
988:C
980:O
974:,
969:n
964:C
959:(
954:1
950:H
943:)
936:n
931:C
923:O
917:,
912:n
907:C
902:(
897:1
893:H
870:n
865:C
843:0
837:)
828:Z
822:,
817:n
812:C
807:(
802:2
798:H
791:)
782:Z
776:,
771:n
766:C
761:(
756:1
752:H
731:)
727:Z
723:;
718:n
713:C
708:(
703:k
695:g
692:n
689:i
686:s
679:H
672:)
663:Z
657:,
652:n
647:C
642:(
637:k
633:H
600:)
591:Z
585:,
580:n
575:C
570:(
565:2
561:H
554:)
542:n
537:C
529:O
523:,
518:n
513:C
508:(
503:1
499:H
492:)
485:n
480:C
472:O
466:,
461:n
456:C
451:(
446:1
442:H
435:)
426:Z
420:,
415:n
410:C
405:(
400:1
396:H
363:0
360:=
357:)
352:n
347:C
342:(
312:n
301:.
299:Z
295:k
290:.
288:Z
284:k
282:(
280:P
265:,
262:)
259:m
256:(
251:O
229:k
225:k
223:(
221:P
213:.
151:.
148:)
138:X
132:O
126:,
123:X
120:(
115:1
111:H
70:X
54:X
50:X
34:.
20:)
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