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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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The BdR+-affine Grassmannian

The BdR+-affine Grassmannian

(p.169) Lecture 19 The BdR+-affine Grassmannian
Berkeley Lectures on p-adic Geometry

Peter Scholze

Jared Weinstein

Princeton University Press

This chapter defines an object that was one of the big motivations to develop a theory of diamonds. In the study of the usual Grassmannian variety G/B attached to a reductive group G, one defines a Schubert variety to be the closure of a B-orbit in G/B. Generally, Schubert varieties are singular varieties. Desingularizations of Schubert varieties are constructed by Demazure. The chapter uses an analogue of this construction in the context of the B+dR-Grassmannian. It then looks at miniscule Schubert varieties. In this case, one can identify the space explicitly. If µ is minuscule, the Bialynicki–Birula map is an isomorphism.

Keywords:   diamonds, Grassmannian variety, Schubert varieties, singular varieties, desingularizations, Demazure, Bialynicki–Birula map, isomorphism

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