Potentially diagonalisable lifts with controlled Hodge-Tate weights
Robin Bartlett
Faculty of Mathematics and Computer Science, University Münster, Einsteinstraße 62, 48149 Münster, Germany
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Abstract
Motivated by the weight part of Serre's conjecture we consider the following question. Let be a finite extension and suppose admits a crystalline lift with Hodge-Tate weights contained in the range . Does admit a potentially diagonalisable crystalline lift of the same Hodge-Tate weights? We answer this question in the affirmative when and , and satisfies a mild 'cyclotomic-free' condition. We also prove partial results when is unramified and is arbitrary.
Cite this article
Robin Bartlett, Potentially diagonalisable lifts with controlled Hodge-Tate weights. Doc. Math. 26 (2021), pp. 795–827
DOI 10.4171/DM/830