Tamagawa number conjecture for a p-adic family of uniform F-crystals

2020/09/28 by Tung T. Nguyen, Nguyen, Tung T.
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2009.13360

openalex publication_date 2020/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

K. Kato has recently constructed certain syntomic complexes associated with a uniform F-crystal over a smooth project variety X and related their cohomology groups to special values of the L-function attached to F. In this paper, we generalize his results to a p-adic family of F-crystals.

Related

• Syntomic complexes of F-crystals and Tamagawa number conjecture in characteristic p, with Appendix by Arthur Ogus
• Tamagawa numbers of some crystalline representations
• p-adic properties of motivic fundamental lines (Kato's conjecture is (probably) false for (not so) trivial reasons)
• On Bloch-Kato's Tamagawa number conjecture for Hecke characters of imaginary quadratic number fields
• On p-adic families of special elements for rank-one motives