On the Picard group: torsion and the kernel
| dc.creator | Guralnick, Robert | |
| dc.creator | Jaffe, David | |
| dc.creator | Raskind, Wayne | |
| dc.creator | Wiegand, Roger | |
| dc.date | 1994-10-31 | |
| dc.date.accessioned | 2026-07-07T09:06:16Z | |
| dc.date.available | 2026-07-07T09:06:16Z | |
| dc.description | For a homomorphism f: A --> B of commutative rings, let D(A,B) denote Ker[Pic(A) --> Pic(B)]. Let k be a field and assume that A is a f.g. k-algebra. We prove a number of finiteness results for D(A,B). Here are four of them. 1: Suppose B is a f.g. and faithfully flat A-algebra which is geometrically integral over k. If k is perfect, we find that D(A,B) is f.g. (In positive characteristic, we need resolution of singularities to prove this.) For an arbitrary field k of positive characteristic p, we find that modulo p-power torsion, D(A,B) is f.g. 2: Suppose B = A tensor k^sep. We find that D(A,B) is finite. 3: Suppose B = A tensor L, where L is a finite, purely inseparable extension. We give examples to show that D(A,B) may be infinite. 4: Assuming resolution of singularities, we show that if K/k is any algebraic extension, there is a finite extension E/k contained in K/k such that D(A tensor E,A tensor K) is trivial. The remaining results are absolute finiteness results for Pic(A). 5: For every n prime to char(k), Pic(A) has only finitely many elements of order n. 6: Structure theorems are given for Pic(A), in the case where k is absolutely f.g. All of these results are proved in a more general form, valid for schemes. Hard copy is available from the authors. | |
| dc.description | 27 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9410031 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9410031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149947 | |
| dc.subject | Algebraic Geometry | |
| dc.title | On the Picard group: torsion and the kernel | |
| dc.type | text |