Mathematical Research Letters

Volume 30 (2023)

Number 5

On certain extensions of vector bundles in $p$-adic geometry

Pages: 1463 – 1483

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n5.a6

Author

Serin Hong (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Abstract

Given two arbitrary vector bundles on the Fargues–Fontaine curve, we give an explicit criterion in terms of Harder–Narasimhan polygons on whether they realize a semistable vector bundle as their extensions. Our argument is largely combinatorial and builds upon the dimension analysis of certain moduli spaces of bundle maps developed in $\href{https://doi.org/10.1017/S1474748020000183}{[1]}$.

Received 23 August 2021

Received revised 23 April 2022

Accepted 17 May 2022

Published 14 May 2024