Weil-etale Cohomology and Special Values of L-functions

2016/11/06 by Minh-Hoang Tran, Tran, Minh-Hoang
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #math.NT #msc:11R29 #msc:11R34 #msc:11S40 #msc:14F20

paper · pdf · doi:10.48550/arxiv.1611.01720

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

arxiv created 2016/11/06 · arxiv updated 2016/11/08

Abstract

We construct the Weil-étale cohomology and Euler characteristics for a subclass of the class of 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 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.

Citations

• Weil-etale cohomology and special values of L-functions at zero

Related

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