Tag - Hodge theory

Will Sawin: The Shafarevich Conjecture for Hypersurfaces in Abelian Varieties

18th March, 2021

Faltings proved the statement, previously conjectured by Shafarevich, that there are finitely many abelian varieties of dimension n, defined over a fixed number field, with good reduction outside a fixed finite set of primes, up to isomorphism. In joint work with Brian Lawrence, we prove an analogous finiteness statement for hypersurfaces in a fixed abelian variety with good reduction outside a finite set of primes. I will give a broad introduction to some of the ideas in the proof, which builds on p-adic Hodge theory techniques from work of Lawrence and Venkatesh as well as sheaf convolution in algebraic geometry.

Koji Shimizu: A p-adic monodromy theorem for de Rham local systems

27th February, 2020

Every smooth proper algebraic variety over a p-adic field is expected to have a semistable model after passing to a finite extension. This conjecture is open in general, but its analogue for Galois representations, the p-adic monodromy theorem, is known. In this talk, we will explain a generalization of this theorem to étale local systems on a smooth rigid analytic variety.

Laurent Fargues: From local class field theory to the curve and vice versa

29th October, 2015

I will speak about results contained in my article "G-torseurs en théorie de Hodge p-adique" linked to local class field theory. I will in particular explain the computation of the Brauer group of the curve and why its fundamental class is the one from local class field theory.