Unit L-functions and a conjecture of Katz
| dc.creator | Emerton, Matthew | |
| dc.creator | Kisin, Mark | |
| dc.date | 2001-03-01 | |
| dc.date.accessioned | 2026-07-07T04:40:53Z | |
| dc.date.available | 2026-07-07T04:40:53Z | |
| dc.description | Let f: X -> Y be a separated morphism of schemes of finite type over a finite field of characteristic p, let Lambda be an artinian local Z_p-algebra with finite residue field, let m be the maximal ideal of Lambda, and let L^\bullet be a bounded constructible complex of sheaves of finite free Lambda-modules on the étale site of Y. We show that the ratio of L-functions L(X,L^\bullet)/L(Y,f_! L^\bullet), which is a priori an element of 1+T Lambda[[T]], in fact lies in 1+ m T Lambda [T]. This implies a conjecture of Katz predicting the location of the zeroes and poles of the L-function of a p-adic étale lisse sheaf on the closed unit disk in terms of étale cohomology with compact support. | |
| dc.description | 26 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0103237 | |
| dc.identifier | http://arxiv.org/abs/math/0103237 | |
| dc.identifier | Ann. of Math. (2) 153 (2001), no. 2, 329--354 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61188 | |
| dc.subject | Number Theory | |
| dc.title | Unit L-functions and a conjecture of Katz | |
| dc.type | text |