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.
Citation
Bergdall, J. & B. Levin. 2022 "Reductions of Some Two-Dimensional Crystalline Representations via Kisin Modules." International Mathematics Research Notices 2022.4: 3170–3197.
DOI
http://doi.org/10.1093/imrn/rnaa240
