Irregular loci in the Emerton–Gee stack for GL<sub>2</sub>-Reference-Cited by-同舟云学术

Irregular loci in the Emerton–Gee stack for GL₂

Published:2024-07-18 Issue: Volume: Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Bellovin Rebecca¹^ORCID,Borade Neelima²^ORCID,Hilado Anton³^ORCID,Kansal Kalyani⁴^ORCID,Lee Heejong⁵^ORCID,Levin Brandon⁶^ORCID,Savitt David⁷^ORCID,Wiersema Hanneke⁸^ORCID

Affiliation:

1. University of Connecticut , Storrs , CT 06269 , USA

2. Princeton University , Fine Hall, Washington Road , Princeton , NJ 08544-1000 , USA

3. University of Vermont , Burlington , VT 05405 , USA

4. Institute for Advanced Study , Princeton , NJ 08540 , USA

5. Purdue University , West Lafayette , IN 47907 , USA

6. Department of Mathematics , Rice University , 6100 Main Street , Houston , TX 77005 , USA

7. 1466 Johns Hopkins University , Baltimore , MD 21218 , USA

8. Centre for Mathematical Sciences , University of Cambridge , Wilberforce Road , Cambridge CB3 0WB , United Kingdom

Abstract

Abstract Let K / Q p

K/\mathbf{Q}_{p}

be unramified. Inside the Emerton–Gee stack X 2

\mathcal{X}_{2}

, one can consider the locus of two-dimensional mod 𝑝 representations of Gal ⁢ ( K ̄ / K )

\mathrm{Gal}(\overline{K}/K)

having a crystalline lift with specified Hodge–Tate weights. We study the case where the Hodge–Tate weights are irregular, which is an analogue for Galois representations of the partial weight one condition for Hilbert modular forms. We prove that if the gap between each pair of weights is bounded by 𝑝 (the irregular analogue of a Serre weight), then this locus is irreducible. We also establish various inclusion relations between these loci.

Funder

National Science Foundation

National Security Agency

Deutsche Forschungsgemeinschaft

Engineering and Physical Sciences Research Council

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0045/pdf

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