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Berkeley Lectures on p-adic Geometry(AMS-207)$
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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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Shtukas with one leg

Shtukas with one leg

(p.98) Lecture 12 Shtukas with one leg
Berkeley Lectures on p-adic Geometry

Peter Scholze

Jared Weinstein

Princeton University Press

This chapter analyzes shtukas with one leg over a geometric point in detail, and discusses the relation to (integral) p-adic Hodge theory. It focuses on the connection between shtukas with one leg and p-divisible groups, and recovers a result of Fargues which states that p-divisible groups are equivalent to one-legged shtukas of a certain kind. In fact this is a special case of a much more general connection between shtukas with one leg and proper smooth (formal) schemes. Throughout, the goal is to fix an algebraically closed nonarchimedean field. The chapter then provides an overview of shtukas with one leg and p-divisible groups.

Keywords:   shtukas, p-adic Hodge theory, p-divisible groups, one-legged shtukas, formal schemes, nonarchimedean field

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