Document Type

Article

Version

Author's Final Manuscript

Publication Title

International Mathematics Research Notices

Volume

2022

Publication Date

2022

Abstract

We determine rational Kisin modules associated with 2-dimensional, irreducible, crystalline representations of Gal(Q¯p/Qp)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Gal(ℚ⎯⎯⎯⎯⎯p/ℚp) of Hodge–Tate weights 0,k−1" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">0,k−1⁠. If the slope is larger than ⌊k−1p⌋" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⌊k−1p⌋⁠, we further identify an integral Kisin module, which we use to calculate the semisimple reduction of the Galois representation. In that range, we find that the reduction is constant, thereby improving on a theorem of Berger, Li, and Zhu.

DOI

http://doi.org/10.1093/imrn/rnaa240

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