Syntomic complex and p-adic nearby cycles

2023/08/21 by Abhinandan
#11S25 #14F20 #14F30 #14F40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2308.10736

Abstract

In local relative p-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the associated F-isocrystal. In global applications, for smooth (p-adic formal) schemes, we establish a comparison between the syntomic complex with coefficients in a locally free Fontaine--Laffaille module and the p-adic nearby cycles of the associated étale local system on the (rigid) generic fibre.

Related

• Syntomic complexes and p-adic nearby cycles
• Local Shtukas, Hodge-Pink Structures and Galois Representations
• Syntomification and crystalline local systems
• An arithmetic étale-crystalline comparison with coefficients in crystalline local systems
• On Fontaine's conjecture for torsion crystalline local systems