G-torsors on perfectoid spaces

2022/07/15 by Ben Heuer, Heuer, Ben
Mathematics · #math.AG

paper · pdf · doi:10.46298/epiga.2026.13796

Abstract

For any rigid analytic group variety G over a non-archimedean field K over \mathbb Q_p, we study G-torsors on adic spaces over K in the v-topology. Our main result is that on perfectoid spaces, G-torsors in the étale and v-topology are equivalent. This generalises the known cases of G=\mathbb G_a and G=GL_n due to Scholze and Kedlaya--Liu. On a general adic space X over K, where there can be more v-topological G-torsors than étale ones, we show that for any open subgroup U⊆ G, any G-torsor on X_v admits a reduction of structure group to U étale-locally on X. This has applications in the context of the p-adic Simpson correspondence: For example, we use it to show that on any adic space, generalised \mathbb Q_p-representations are equivalent to v-vector bundles.

Related

• Characterizing perfectoid covers of abelian varieties
• Moduli spaces in p-adic non-abelian Hodge theory
• G-torsors and universal torsors over nonsplit del Pezzo surfaces
• G-torsors over a Dedekind scheme
• Line bundles on rigid spaces in the v-topology