Breuil-Mézard conjectures for central division algebras
Breuil-Mézard conjectures for central division algebras
复制标题
中心除代数的布勒伊-梅扎德猜想
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Andrea Dotto
中科院分区：
文献类型：
--
作者：
Andrea Dotto
本文给出了$p$一元局部域上中心除法代数单元群的Breuil-M'ezard猜想的一个类比，并证明了它是$ mathm {GL}_n$猜想的推导。为此，我们根据Deligne-Lusztig理论在这两个群的最大紧子群之间构造了惯性类型和Serre权的转移，并通过惯性Jacquet-Langlands对应和某些显式特征公式证明了它与mod $p$约简的相容性。我们还证明了$ell$-adic系数的类似命题。
We formulate an analogue of the Breuil-M'ezard conjecture for the group of units of a central division algebra over a $p$-adic local field, and we prove that it follows from the conjecture for $mathrm{GL}_n$. To do so we construct a transfer of inertial types and Serre weights between the maximal compact subgroups of these two groups, in terms of Deligne-Lusztig theory, and we prove its compatibility with mod $p$ reduction, via the inertial Jacquet-Langlands correspondence and certain explicit character formulas. We also prove analogous statements for $ell$-adic coefficients.