Syntomic cohomology and p-adic motivic cohomology

2016/03/05 by Veronika Ertl, Ertl, Veronika, Wiesława Nizioł +1 · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1603.01705

Abstract

We prove a mixed characteristic analog of the Beilinson-Lichtenbaum Conjecture for p-adic motivic cohomology. It gives a description, in the stable range, of p-adic motivic cohomology (defined using algebraic cycles) in terms of differential forms. This generalizes a result of Geisser from small Tate twists to all twists and uses as a critical new ingredient the comparison theorem between syntomic complexes and p-adic nearby cycles proved recently in Colmez-Niziol.

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