Filtrations of Barsotti-Tate groups via Harder-Narasimhan theory.

Abstract: Let $p$ be a prime number and let $R$ be a complete valuation ring of rank one and mixed characteristic $(0,p)$. Given a Barsotti-Tate group $H$ over $R$, its $p$-power-torsion parts possess a natural "Harder-Narasimhan" filtration, introduced by Fargues in analogy with the theory of vector bundles over a smooth projective curve over an algebraically closed field. One may wonder when these filtrations build up to a filtration of the whole Barsotti-Tate group $H$. I will present some sufficient conditions in this direction, especially in the case that the endomorphisms of $H$ contain the ring of integers of a finite extension of $\mathbb{Q}_p$. This is partly based on a joint work with Stéphane Bijakowski.

algebraic geometrynumber theory

Audience: researchers in the topic

Number Theory Seminars at Università degli Studi di Padova