2024/11/12 by Adrien Morin, Morin, Adrien
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2411.07896
openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a variety over a finite field. Given an order R in a semi-simple algebra over the rationals and a constructible étale 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-étale 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.