Harder-Narasimhan strata and 𝑝-adic period domains

Abstract

We revisit the Harder-Narasimhan stratification on a minuscule p p -adic flag variety, by the theory of modifications of G G -bundles on the Fargues-Fontaine curve. We compare the Harder-Narasimhan strata with the Newton strata introduced by Caraiani-Scholze. As a consequence, we get further equivalent conditions in terms of p p -adic Hodge-Tate period domains for fully Hodge-Newton decomposable pairs. Moreover, we generalize these results to arbitrary cocharacters case by considering the associated B d R + B_{dR}^+ -affine Schubert varieties. Applying Hodge-Tate period maps, our constructions give applications to p p -adic geometry of Shimura varieties and their local analogues.