Weil-etale Cohomology and Special Values of L-functions

Abstract

We construct the Weil-étale cohomology and Euler characteristics for a subclass of the class of $\mathbb{Z}$-constructible sheaves on an open subscheme of the spectrum of the ring of integers of a number field. Then we show that the special value of an Artin L-function of toric type at zero is given by the Weil-étale Euler characteristic of an appropriate $\mathbb{Z}$-constructible sheaf up to signs. As applications of our result, we will prove a formula for the special value of the L-function of an algebraic torus at zero which is similar to Ono's Tamagawa Number Formula.

Replace an earlier paper with major revision to treat the non-totally imaginary number field case and special values of partial L-functions. arXiv admin note: text overlap with arXiv:1608.01152

Cited by in corpus (2)

• Special values of $L$-functions on regular arithmetic schemes of dimension $1$
• Tori over number fields and special values at s=1