Combinatorics of Serre weights in the potentially Barsotti-Tate setting
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
DAVID, Agnès
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Recherche Mathématique de Rennes [IRMAR]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Recherche Mathématique de Rennes [IRMAR]
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
DAVID, Agnès
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Recherche Mathématique de Rennes [IRMAR]
< Reduce
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Recherche Mathématique de Rennes [IRMAR]
Language
en
Article de revue
This item was published in
Moscow Journal of Combinatorics and Number Theory. 2023, vol. 12, n° 1, p. 1 - 56
Moscow Institute of Physics and Technology
English Abstract
Let $F$ be a finite unramified extension of $\mathbb Q_p$ and $\bar\rho$ be an absolutely irreducible mod~$p$ $2$-dimensional representation of the absolute Galois group of $F$. Let $t$ be a tame inertial type of $F$. We ...Read more >
Let $F$ be a finite unramified extension of $\mathbb Q_p$ and $\bar\rho$ be an absolutely irreducible mod~$p$ $2$-dimensional representation of the absolute Galois group of $F$. Let $t$ be a tame inertial type of $F$. We conjecture that the deformation space parametrizing the potentially Barsotti--Tate liftings of $\bar\rho$ having type $t$ depends only on the Kisin variety attached to the situation, enriched with its canonical embedding into $(\mathbb P^1)^f$ and its shape stratification. We give evidences towards this conjecture by proving that the Kisin variety determines the cardinality of the set of common Serre weights $D(t,\bar\rho) = D(t) \cap D(\bar\rho)$. Besides, we prove that this dependance is nondecreasing (the smaller is the Kisin variety, the smaller is the number of common Serre weights) and compatible with products (if the Kisin variety splits as a product, so does the number of weights).Read less <
ANR Project
Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
Hal imported