اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGeometrization of continuous characters of $mathbb{Z}_p^times$
195
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We define the $p$-adic trace of certain rank-one local systems on the multiplicative group over $p$-adic numbers, using Sekiguchi and Suwas unification of Kummer and Artin-Schrier-Witt theories. Our main observation is that, for every non-negative integer $n$, the $p$-adic trace defines an isomorphism of abelian groups between local systems whose order divides $(p-1)p^n$ and $ell$-adic characters of the multiplicative group of $p$-adic integers of depth less than or equal to $n$.
قيم البحث
اقرأ أيضاً
For every pair of distinct primes $p$, $q$ we prove that $mathbb{Z}_p^3 times mathbb{Z}_q$ is a CI-group with respect to binary relational structures.
Following the ideas of Ginzburg, for a subgroup $K$ of a connected reductive $mathbb{R}$-group $G$ we introduce the notion of $K$-admissible $D$-modules on a homogeneous $G$-variety $Z$. We show that $K$-admissible $D$-modules are regular holonomic w
hen $K$ and $Z$ are absolutely spherical. This framework includes: (i) the relative characters attached to two spherical subgroups $H_1$ and $H_2$, provided that the twisting character $chi_i$ factors through the maximal reductive quotient of $H_i$, for $i = 1, 2$; (ii) localization on $Z$ of Harish-Chandra modules; (iii) the generalized matrix coefficients when $K(mathbb{R})$ is maximal compact. This complements the holonomicity proven by Aizenbud--Gourevitch--Minchenko. The use of regularity is illustrated by a crude estimate on the growth of $K$-admissible distributions which based on tools from subanalytic geometry.
We provide a number of new conjectures and questions concerning the syzygies of $mathbb{P}^1times mathbb{P}^1$. The conjectures are based on computing the graded Betti tables and related data for large number of different embeddings of $mathbb{P}^1ti
mes mathbb{P}^1$. These computations utilize linear algebra over finite fields and high-performance computing.
This is the sequel to arXiv:2007.01364v1. Let $F$ be any local field with residue characteristic $p>0$, and $mathcal{H}^{(1)}_{overline{mathbb{F}}_p}$ be the mod $p$ pro-$p$-Iwahori Hecke algebra of $mathbf{GL_2}(F)$. In arXiv:2007.01364v1 we have co
nstructed a parametrization of the $mathcal{H}^{(1)}_{overline{mathbb{F}}_p}$-modules by certain $widehat{mathbf{GL_2}}(overline{mathbb{F}}_p)$-Satake parameters, together with an antispherical family of $mathcal{H}^{(1)}_{overline{mathbb{F}}_p}$-modules. Here we let $F=mathbb{Q}_p$ (and $pgeq 5$) and construct a morphism from $widehat{mathbf{GL_2}}(overline{mathbb{F}}_p)$-Satake parameters to $widehat{mathbf{GL_2}}(overline{mathbb{F}}_p)$-Langlands parameters. As a result, we get a version in families of Breuils semisimple mod $p$ Langlands correspondence for $mathbf{GL_2}(mathbb{Q}_p)$ and of Pav{s}k={u}nas parametrization of blocks of the category of mod $p$ locally admissible smooth representations of $mathbf{GL_2}(mathbb{Q}_p)$ having a central character. The formulation of these results is possible thanks to the Emerton-Gee moduli space of semisimple $widehat{mathbf{GL_2}}(overline{mathbb{F}}_p)$-representations of the Galois group ${rm Gal}(overline{mathbb{Q}}_p/ mathbb{Q}_p)$.
We apply the theory of fundamental strata of Bremer and Sage to find cohomologically rigid $G$-connections on the projective line, generalising the work of Frenkel and Gross. In this theory, one studies the leading term of a formal connection with re
spect to the Moy-Prasad filtration associated to a point in the Bruhat-Tits building. If the leading term is regular semisimple with centraliser a (not necessarily split) maximal torus $S$, then we have an $S$-toral connection. In this language, the irregular singularity of the Frenkel-Gross connection gives rise to the homogenous toral connection of minimal slope associated to the Coxeter torus $mathcal{C}$. In the present paper, we consider connections on $mathbb{G}_m$ which have an irregular homogeneous $mathcal{C}$-toral singularity at zero of slope $i/h$, where $h$ is the Coxeter number and $i$ is a positive integer coprime to $h$, and a regular singularity at infinity with unipotent monodromy. Our main result is the characterisation of all such connections which are rigid.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
