Contents Online
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
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