Irregular loci in the Emerton-Gee stack for GL2

Rebecca Bellovin; Neelima Borade; Anton Hilado; Kalyani Kansal; Heejong Lee; Brandon Levin; David Savitt; Hanneke Wiersema

doi:10.1515/crelle-2024-0045

Irregular loci in the Emerton-Gee stack for GL₂

Rebecca Bellovin, Neelima Borade, Anton Hilado, Kalyani Kansal, Heejong Lee, Brandon Levin, David Savitt, Hanneke Wiersema

Research output: Contribution to journal › Article › peer-review

Abstract

Let K / Q_p be unramified. Inside the Emerton-Gee stack X₂, one can consider the locus of two-dimensional mod p representations of Gal(K̄/ 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.

Original language	English (US)
Journal	Journal fur die Reine und Angewandte Mathematik
DOIs	https://doi.org/10.1515/crelle-2024-0045
State	Accepted/In press - 2024
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/crelle-2024-0045

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title = "Irregular loci in the Emerton-Gee stack for GL2",

abstract = "Let K / Qp be unramified. Inside the Emerton-Gee stack X2, one can consider the locus of two-dimensional mod p representations of Gal({\=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.",

author = "Rebecca Bellovin and Neelima Borade and Anton Hilado and Kalyani Kansal and Heejong Lee and Brandon Levin and David Savitt and Hanneke Wiersema",

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doi = "10.1515/crelle-2024-0045",

language = "English (US)",

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T1 - Irregular loci in the Emerton-Gee stack for GL2

AU - Bellovin, Rebecca

AU - Borade, Neelima

AU - Hilado, Anton

AU - Kansal, Kalyani

AU - Lee, Heejong

AU - Levin, Brandon

AU - Savitt, David

AU - Wiersema, Hanneke

PY - 2024

Y1 - 2024

N2 - Let K / Qp be unramified. Inside the Emerton-Gee stack X2, one can consider the locus of two-dimensional mod p representations of Gal(K̄/ 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.

AB - Let K / Qp be unramified. Inside the Emerton-Gee stack X2, one can consider the locus of two-dimensional mod p representations of Gal(K̄/ 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.

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ER -

Irregular loci in the Emerton-Gee stack for GL₂

Abstract

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