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  Degenerating products of flag varieties and applications to the Breuil-Mézard conjecture

Bartlett, R. (2024). Degenerating products of flag varieties and applications to the Breuil-Mézard conjecture. Selecta Mathematica, 30(1): 17. doi:10.1007/s00029-023-00905-3.

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Bartlett, Robin1, Author                 
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory, Algebraic Geometry, Representation Theory
 Abstract: We consider closed subschemes in the affine grassmannian obtained by degenerating $e$-fold products of flag varieties, embedded via a tuple of dominant cocharacters. For $G= \operatorname{GL}_2$, and cocharacters small relative to the characteristic, we relate the cycles of these degenerations to the representation theory of $G$. We then show that these degenerations smoothly model the geometry of (the special fibre of) low weight crystalline subspaces inside the Emerton--Gee stack classifying $p$-adic representations of the Galois group of a finite extension of $\mathbb{Q}_p$. As an application we
prove new cases of the Breuil--M\'ezard conjecture in dimension two.

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Language(s): eng - English
 Dates: 2024
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 2108.04094
DOI: 10.1007/s00029-023-00905-3
 Degree: -

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Title: Selecta Mathematica
Source Genre: Journal
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Publ. Info: Birkhäuser
Pages: 48 Volume / Issue: 30 (1) Sequence Number: 17 Start / End Page: - Identifier: -