Syntomic cohomology and period morphisms

Abstract: In 2017, Colmez and Niziol proved a comparison theorem between arithmetic $p$-adic nearby cycles and syntomic cohomology sheaves. To prove it, they gave a local construction using $(\phi, \Gamma)$-modules theory which allows to reduce the period isomorphism to a comparison theorem between cohomologies of Lie algebras. I will explain the geometric version of this local construction and how to globalize it to get a new period isomorphism. In particular, the explicit description of this new isomorphism can be used to compare previous constructions of period morphisms and prove they are equal.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar