Harder-Narasimhan strata and p-adic period domains

2019/09/05 by Xu Shen, Shen, Xu
Arts and Humanities · Mathematics · #11G18 #14G20 #14G35 #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis

paper · pdf · doi:10.48550/arxiv.1909.02230

openalex publication_date 2019/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the Harder-Narasimhan stratification on a minuscule p-adic flag variety, by the theory of modifications of 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-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_dR⁺-affine Schubert varieties. Applying Hodge-Tate period maps, our constructions give applications to p-adic geometry of Shimura varieties and their local analogues.

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