English

Weil-etale Cohomology and Special Values of L-functions

Number Theory 2016-11-08 v1

Abstract

We construct the Weil-\'etale cohomology and Euler characteristics for a subclass of the class of Z\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-\'etale Euler characteristic of an appropriate Z\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.

Keywords

Cite

@article{arxiv.1611.01720,
  title  = {Weil-etale Cohomology and Special Values of L-functions},
  author = {Minh-Hoang Tran},
  journal= {arXiv preprint arXiv:1611.01720},
  year   = {2016}
}

Comments

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