Weil-\'etale cohomology and the equivariant Tamagawa number conjecture for constructible sheaves in characteristic $p$

Autor:	Morin, Adrien
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	Let $X$ be a variety over a finite field. Given an order $R$ in a semi-simple algebra over the rationals and a constructible \'etale sheaf $F$ of $R$-modules over $X$, one can consider a natural non-commutative $L$-function associated with $F$. We prove a special value formula at negative integers for this $L$-function, expressed in terms of Weil-\'etale cohomology; this is a geometric analogue of, and implies, the equivariant Tamagawa number conjecture for an Artin motive and its negative twists over a global function field. It also generalizes the results of Lichtenbaum and Geisser on special values at negative integers for zeta functions of varieties, and the work of Burns--Kakde in the case of non-commutative L-functions coming from a Galois cover of varieties. Comment: 36 pages, comments welcome !
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.07896 Zobrazit plný text záznamu View this record from Arxiv