Knowledge (XXG)

Morphism of finite type

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540: 233: 222: 581: 574: 250: 610: 525: 124: 567: 245: 600: 435: 497: 56: 79: 420: 459: 271: 87: 377: 44: 17: 605: 547: 521: 467: 21: 551: 474: 392: 32: 517: 509: 99: 594: 298: 384: 539: 301: 275: 121:= 0. Another example of a finite-type homomorphism that is not finite is 226: 217:{\displaystyle \mathbb {C} \to \mathbb {C} /(y^{2}-x^{3}-t)} 555: 127: 438:says, in geometric terms, that every affine scheme 329:) has a finite covering by affine open subschemes 216: 473:over a field has a finite surjective morphism to 446:has a finite surjective morphism to affine space 109:-algebra of finite type, but it is not a finite 575: 242:needs attention from an expert in Mathematics 8: 357:-algebra of finite type. One also says that 582: 568: 514:Algebraic Geometry and Commutative Algebra 199: 186: 174: 146: 145: 129: 128: 126: 90:. For example, for any commutative ring 253:may be able to help recruit an expert. 7: 536: 534: 372:For example, for any natural number 554:. You can help Knowledge (XXG) by 411:), while they are not finite over 63:-algebra. It is much stronger for 14: 270:The analogous notion in terms of 538: 231: 211: 179: 171: 159: 156: 150: 142: 139: 133: 1: 442:of finite type over a field 436:Noether normalization lemma 74:-algebra, which means that 627: 533: 498:Finitely generated algebra 419:= 0. More generally, any 611:Algebraic geometry stubs 403:are of finite type over 427:is of finite type over 421:quasi-projective scheme 251:WikiProject Mathematics 550:โ€“related article is a 218: 219: 520:. pp. 360โ€“365. 484:is the dimension of 407:(that is, over Spec 125: 94:and natural number 18:commutative algebra 601:Algebraic geometry 548:algebraic geometry 466:. Likewise, every 297:has a covering by 214: 80:finitely generated 57:finitely generated 563: 562: 468:projective scheme 289:of schemes is of 268: 267: 33:commutative rings 618: 584: 577: 570: 542: 535: 531: 510:Bosch, Siegfried 475:projective space 263: 260: 254: 235: 234: 227: 223: 221: 220: 215: 204: 203: 191: 190: 178: 149: 132: 626: 625: 621: 620: 619: 617: 616: 615: 591: 590: 589: 588: 528: 508: 506: 494: 355: 348: 341: 334: 327: 316: 309: 264: 258: 255: 249: 236: 232: 195: 182: 123: 122: 113:-module unless 100:polynomial ring 12: 11: 5: 624: 622: 614: 613: 608: 603: 593: 592: 587: 586: 579: 572: 564: 561: 560: 543: 526: 505: 502: 501: 500: 493: 490: 353: 346: 339: 332: 325: 314: 307: 266: 265: 239: 237: 230: 213: 210: 207: 202: 198: 194: 189: 185: 181: 177: 173: 170: 167: 164: 161: 158: 155: 152: 148: 144: 141: 138: 135: 131: 13: 10: 9: 6: 4: 3: 2: 623: 612: 609: 607: 604: 602: 599: 598: 596: 585: 580: 578: 573: 571: 566: 565: 559: 557: 553: 549: 544: 541: 537: 532: 529: 527:9781447148289 523: 519: 515: 511: 503: 499: 496: 495: 491: 489: 487: 483: 479: 476: 472: 469: 465: 461: 457: 453: 449: 445: 441: 437: 432: 430: 426: 422: 418: 414: 410: 406: 402: 398: 396: 390: 388: 382: 379: 375: 370: 368: 364: 360: 356: 349: 342: 335: 328: 321: 317: 310: 303: 300: 296: 292: 288: 284: 280: 277: 273: 262: 252: 247: 243: 240:This article 238: 229: 228: 225: 208: 205: 200: 196: 192: 187: 183: 175: 168: 165: 162: 153: 136: 120: 116: 112: 108: 104: 101: 97: 93: 89: 85: 81: 77: 73: 70: 66: 62: 58: 54: 50: 46: 42: 39:is called an 38: 34: 30: 26: 23: 19: 556:expanding it 545: 513: 507: 485: 481: 477: 470: 463: 455: 451: 447: 443: 439: 433: 428: 424: 416: 412: 408: 404: 400: 394: 386: 380: 373: 371: 366: 362: 358: 351: 344: 337: 330: 323: 319: 312: 305: 294: 290: 286: 282: 278: 269: 256: 248:for details. 241: 118: 114: 110: 106: 102: 95: 91: 83: 75: 71: 68: 64: 60: 52: 48: 40: 36: 28: 24: 22:homomorphism 15: 393:projective 363:finite type 304:subschemes 291:finite type 259:August 2023 244:. See the 49:finite type 595:Categories 516:. London: 504:References 318:such that 20:, given a 606:Morphisms 460:dimension 246:talk page 206:− 193:− 143:→ 518:Springer 512:(2013). 492:See also 480:, where 454:, where 276:morphism 67:to be a 458:is the 415:unless 385:affine 336:= Spec 311:= Spec 272:schemes 117:= 0 or 45:algebra 524:  397:-space 389:-space 361:is of 299:affine 274:is: a 105:is an 98:, the 88:module 82:as an 69:finite 59:as an 546:This 450:over 423:over 399:over 378:field 365:over 343:with 55:is a 552:stub 522:ISBN 434:The 391:and 376:and 302:open 462:of 350:an 293:if 78:is 51:if 47:of 31:of 16:In 597:: 488:. 431:. 383:, 369:. 347:ij 340:ij 333:ij 285:โ†’ 281:: 224:. 35:, 27:โ†’ 583:e 576:t 569:v 558:. 530:. 486:X 482:n 478:P 471:X 464:X 456:n 452:k 448:A 444:k 440:X 429:k 425:k 417:n 413:k 409:k 405:k 401:k 395:n 387:n 381:k 374:n 367:Y 359:X 354:i 352:A 345:B 338:B 331:U 326:i 324:V 322:( 320:f 315:i 313:A 308:i 306:V 295:Y 287:Y 283:X 279:f 261:) 257:( 212:) 209:t 201:3 197:x 188:2 184:y 180:( 176:/ 172:] 169:y 166:, 163:x 160:[ 157:] 154:t 151:[ 147:C 140:] 137:t 134:[ 130:C 119:n 115:A 111:A 107:A 103:A 96:n 92:A 86:- 84:A 76:B 72:A 65:B 61:A 53:B 43:- 41:A 37:B 29:B 25:A

Index

commutative algebra
homomorphism
commutative rings
algebra
finitely generated
finitely generated
module
polynomial ring
talk page
WikiProject Mathematics
schemes
morphism
affine
open
field
affine n-space
projective n-space
quasi-projective scheme
Noether normalization lemma
dimension
projective scheme
projective space
Finitely generated algebra
Bosch, Siegfried
Springer
ISBN
9781447148289
Stub icon
algebraic geometry
stub

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