Hodge-Tate stacks and non-abelian p-adic Hodge theory of v-perfect complexes on rigid spaces

2023/02/24 by Anschütz, Johannes, Heuer, Ben, Bras, Arthur-César Le
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.12747

Abstract

Let X be a quasi-compact quasi-separated p-adic formal scheme that is smooth either over a perfectoid ℤ_p-algebra or over some ring of integers of a p-adic field. We construct a fully faithful functor from perfect complexes on the Hodge-Tate stack of X up to isogeny to perfect complexes on the v-site of the generic fibre of X. Moreover, we describe perfect complexes on the Hodge-Tate stack in terms of certain derived categories of Higgs, resp. Higgs-Sen modules. This leads to a derived p-adic Simpson functor.

Related

• Moduli spaces in p-adic non-abelian Hodge theory
• Line bundles on rigid spaces in the v-topology
• Admissible pairs and p-adic Hodge structures I: Transcendence of the de Rham lattice
• The small p-adic Simpson correspondence in terms of moduli spaces
• A geometric p-adic Simpson correspondence in rank one