Potential diagonalisability of pseudo-Barsotti-Tate representations

Bartlett, Robin

doi:10.5802/jtnb.1248

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Potential diagonalisability of pseudo-Barsotti-Tate representations

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Bartlett, Robin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2001.08660
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https://doi.org/10.5802/jtnb.1248
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Bartlett_Potential diagonalisability of pseudo-Barsotti-Tate representations_2023.pdf
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Citation

Bartlett, R. (2023). Potential diagonalisability of pseudo-Barsotti-Tate representations. Journal de Théorie des Nombres de Bordeaux, 35(2), 335-371. doi:10.5802/jtnb.1248.

Cite as: https://hdl.handle.net/21.11116/0000-000D-F3AE-D

Abstract

Previous work of Kisin and Gee proves potential diagonalisability
of two dimensional Barsotti–Tate representations of the Galois group of a
finite extension K/Qp. In this paper we build upon their work by relaxing the
Barsotti–Tate condition to one we call pseudo-Barsotti–Tate (which means
that for certain embeddings κ : K → Qp we allow the κ-Hodge–Tate weights
to be contained in [0, p] rather than [0, 1]).