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## Peter Scholze and Jared Weinstein

Print publication date: 2020

Print ISBN-13: 9780691202082

Published to Princeton Scholarship Online: January 2021

DOI: 10.23943/princeton/9780691202082.001.0001

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# Vector bundles and G-torsors on the relative Fargues-Fontaine curve

Chapter:
(p.207) Lecture 22 Vector bundles and G-torsors on the relative Fargues-Fontaine curve
Source:
Berkeley Lectures on p-adic Geometry
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691202082.003.0022

This chapter discusses vector bundles and G-torsors on the relative Fargues-Fontaine curve. This is in preparation for the examination of moduli spaces of shtukas. Kedlaya-Liu prove two important foundational theorems about vector bundles on the Fargues-Fontaine curve. The first is the semicontinuity of the Newton polygon. The second theorem of Kedlaya-Liu concerns the open locus where the Newton polygon is constant 0. For the applications to the moduli spaces of shtukas, one needs to generalize the results to the case of G-torsors for a general reductive group G. The chapter then identifies the classification of G-torsors. It also looks at the semicontinuity of the Newton point.

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