84:
74:
53:
22:
341:
Thanks for your replies! -- That (connection to slice cat.) does indeed help me a little -- I just had a little 'semantic uneasiness' with the formulation 'all etale morphisms from a scheme to X' -- it might wrongly convey 'from (just) one specific scheme to X'... but disregard this at will, if it
387:
Yes, that is how I understood it, my confusion was that 'Torsion can occur' right after discussion of the 'rational coefficients' (where torsion doesn't occur) seems misleading, i.e., would it not be better, e.g., to swap these last two paragraphs ?
314:
X with f,S (and X) in the category of schemes (category of schemes: also Large?) such that f is etale (perhaps also: is there a (perhaps even full or faithful) functor from the category of schemes to Et(X) ? if yes, would seem helpful to
408:
Calculation: the G_{m,K} in the first exact sequence is not explained anywhere; a few lines below: why the mention of Z_x is made is not fully clear; also there seem to be some minor notation imprecisions (like cursive/non-cursive
308:
I found much help in understanding Et.Coh. from the entry, but also had some questions that maybe one who is confident in these matters may consider if they should be addressed/clarified in the article, e.g.:
179:
In mathematics, the étale cohomology theory of algebraic geometry is a refined construction of homological algebra, introduced by
Alexander Grothendieck as a cohomological tool to attack the Weil conjectures.
362:
Re the last paragraph of the l-adic cohomology section: this is confusing in combination with the paragraph just before it (no torsion, then torsion); I guess it does not refer to the Q_l construction?
140:
277:
313:
Definition of Et(X): I would appreciate if there were a just slightly more explicit/formal definition of objects and arrows - e.g., is this true: the objects are morphisms f:S-: -->
493:
In the article, it is mentioned that the sheaf Q_l is not etale. But it seems to me that it is just the constant sheaf, which is etale. Please help me out with this confusion.
203:
I think it comes from the fact that an etale map is analogous to a local diffeomorphism, so if you draw a curve X etale over Y, this looks pretty much spread out...
438:
I have seen the definition of G_m, just in the lines before, my concern was about the G_{m,K} ... (again, disregard, if this should be clear to the typical reader)
557:
279:
more standard for the sheaf of nonzero functions than G_m? My first guess would have been that H^i(X,G_m) meant cohomology with coefficients in a torus.
130:
106:
552:
189:
500:
157:
Note on the lower case redirect - I thought there was a possible bug, meaning that lower case e-acute wasn't automatically sent to this
529:
289:
188:
Hi, I'm sorry if the information is in the article, but why is the concept called etale? I think this means spread in French. Thanks.
97:
58:
424:, but it is defined in the section as an actual sheaf (i.e. a functor form of taking invertible elements of (whatever)).
33:
520:
429:
378:
332:
228:
208:
246:
193:
175:
well, before editting the page, i wanted to inform that i want to chamge the first sentence to the following:
504:
533:
373:: torsion can occur when the coefficients are integers, but not when the coefficients are rational numbers.
293:
425:
374:
328:
164:
39:
83:
525:
496:
421:
285:
224:
204:
21:
479:
461:
443:
393:
370:
347:
105:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
89:
73:
52:
483:
465:
336:
475:
457:
439:
389:
343:
324:
220:
546:
521:
https://mathoverflow.net/questions/281359/computing-the-etale-cohomology-of-spheres
537:
508:
447:
433:
397:
382:
351:
297:
232:
212:
197:
102:
79:
474:
for the changes (addressing points 2 and part of 3)! I think it's better :)
471:
323:
X that are etale. No functors around such as you mention. It is inside a
519:
An interesting computation which should be added in detail is
15:
253:
161:
page. Well, I encountered a problem with this, yesterday.
171:
where is the name of grothendieck in the very beginning?
243:
I'm no expert so I haven't edited the page, but isn't
249:
101:, a collaborative effort to improve the coverage of
322:Yes, etale morphisms to X means morphisms S -: -->
271:
327:of all morphisms to X, if you want more detail.
8:
523:
272:{\displaystyle {\mathcal {O}}_{X}^{\ast }}
47:
263:
258:
252:
251:
248:
49:
19:
7:
95:This article is within the scope of
38:It is of interest to the following
14:
558:Mid-priority mathematics articles
115:Knowledge:WikiProject Mathematics
369:Makes sense by analogy with say
118:Template:WikiProject Mathematics
82:
72:
51:
20:
135:This article has been rated as
538:01:39, 18 September 2017 (UTC)
1:
109:and see a list of open tasks.
553:B-Class mathematics articles
298:09:11, 3 October 2009 (UTC)
574:
233:11:49, 14 March 2008 (UTC)
213:11:49, 14 March 2008 (UTC)
198:23:08, 13 March 2008 (UTC)
509:01:19, 11 June 2012 (UTC)
484:16:49, 14 June 2011 (UTC)
167:11:04, 14 Dec 2003 (UTC)
134:
67:
46:
466:14:03, 8 June 2011 (UTC)
448:15:18, 8 June 2011 (UTC)
434:14:53, 8 June 2011 (UTC)
420:notation is usually the
398:15:18, 8 June 2011 (UTC)
383:14:53, 8 June 2011 (UTC)
352:15:18, 8 June 2011 (UTC)
337:14:48, 8 June 2011 (UTC)
304:from a learner's pov ...
141:project's priority scale
303:
98:WikiProject Mathematics
273:
28:This article is rated
274:
223:for the terminology.
422:multiplicative group
342:seems clear enough.
247:
239:question on notation
121:mathematics articles
371:singular cohomology
268:
269:
250:
90:Mathematics portal
34:content assessment
540:
528:comment added by
499:comment added by
288:comment added by
155:
154:
151:
150:
147:
146:
565:
511:
426:Charles Matthews
375:Charles Matthews
329:Charles Matthews
300:
278:
276:
275:
270:
267:
262:
257:
256:
165:Charles Matthews
159:Étale cohomology
123:
122:
119:
116:
113:
92:
87:
86:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
573:
572:
568:
567:
566:
564:
563:
562:
543:
542:
517:
494:
491:
419:
306:
283:
245:
244:
241:
225:Jakob.scholbach
205:Jakob.scholbach
186:
173:
120:
117:
114:
111:
110:
88:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
571:
569:
561:
560:
555:
545:
544:
516:
513:
490:
487:
455:
454:
453:
452:
451:
450:
417:
411:
410:
405:
404:
403:
402:
401:
400:
364:
363:
359:
358:
357:
356:
355:
354:
325:slice category
317:
316:
305:
302:
266:
261:
255:
240:
237:
236:
235:
221:etale morphism
216:
215:
190:131.111.216.28
185:
182:
172:
169:
153:
152:
149:
148:
145:
144:
133:
127:
126:
124:
107:the discussion
94:
93:
77:
65:
64:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
570:
559:
556:
554:
551:
550:
548:
541:
539:
535:
531:
527:
522:
514:
512:
510:
506:
502:
501:77.13.108.173
498:
488:
486:
485:
481:
477:
473:
468:
467:
463:
459:
449:
445:
441:
437:
436:
435:
431:
427:
423:
415:
414:
413:
412:
407:
406:
399:
395:
391:
386:
385:
384:
380:
376:
372:
368:
367:
366:
365:
361:
360:
353:
349:
345:
340:
339:
338:
334:
330:
326:
321:
320:
319:
318:
312:
311:
310:
301:
299:
295:
291:
287:
280:
264:
259:
238:
234:
230:
226:
222:
218:
217:
214:
210:
206:
202:
201:
200:
199:
195:
191:
183:
181:
180:
176:
170:
168:
166:
162:
160:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
530:70.59.17.182
524:— Preceding
518:
515:Computations
495:— Preceding
492:
469:
456:
307:
290:85.225.79.77
281:
242:
187:
178:
177:
174:
163:
158:
156:
137:Mid-priority
136:
96:
62:Mid‑priority
40:WikiProjects
489:Etale Sheaf
284:—Preceding
112:Mathematics
103:mathematics
59:Mathematics
547:Categories
470:Thanks to
184:why etale?
476:Summsumm2
458:Summsumm2
440:Summsumm2
390:Summsumm2
344:Summsumm2
526:unsigned
497:unsigned
315:mention)
286:unsigned
139:on the
30:B-class
282:/dan
36:scale.
416:The G
534:talk
505:talk
480:talk
472:Ozob
462:talk
444:talk
430:talk
394:talk
379:talk
348:talk
333:talk
294:talk
229:talk
219:See
209:talk
194:talk
131:Mid
549::
536:)
507:)
482:)
464:)
446:)
432:)
409:K)
396:)
381:)
350:)
335:)
296:)
265:∗
231:)
211:)
196:)
532:(
503:(
478:(
460:(
442:(
428:(
418:m
392:(
377:(
346:(
331:(
292:(
260:X
254:O
227:(
207:(
192:(
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
