Abstract
Let \(K_0/\mathbb {Q}_p\) be a finite unramified extension, \(G_{K_0}\) the Galois group \(\text {Gal}(\overline{\mathbb {Q}}_p/K_0)\). We show that all crystalline representations of \(G_{K_0}\) with Hodge-Tate weights \(\subseteq \{0, \ldots , p-1\}\) are potentially diagonalizable.
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Acknowledgments
It is a pleasure to thank David Geraghty and Toby Gee for very useful conversations and correspondence. We also would like to thank the anonymous referee for helping to improve the exposition.
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The second author is partially supported by NSF grant DMS-0901360.
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Gao, H., Liu, T. A note on potential diagonalizability of crystalline representations. Math. Ann. 360, 481–487 (2014). https://doi.org/10.1007/s00208-014-1041-7
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DOI: https://doi.org/10.1007/s00208-014-1041-7