2022/01/11 by Tim Dokchitser, Vladimir Dokchitser, Dokchitser, Tim +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11F80 #11G10 #11G20 #11G25 #14F20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2201.04094
openalex publication_date 2022/01/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
It is known that the etale cohomology of a potentially good abelian variety over a local field K is determined by its Euler factors over the extensions of K. We extend this to all abelian varieties, show that it is enough to take extensions where A is semistable, and give a uniform version over p-adic fields where the extensions are the same for all abelian varieties of a given dimension. The results are explicit, and apply to a wide class of Weil-Deligne representations.