اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدArithmetic and Differential Swan Conductors of rank one representations with finite local monodromy
79
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider a complete discrete valuation field of characteristic p, with possibly non perfect residue field. Let V be a rank one continuous representation with finite local monodromy of its absolute Galois group. We will prove that the Arithmetic Swan conductor of V (defined after Kato in [Kat89] which fits in the more general theory of [AS02] and [AS06]) coincides with the Differential Swan conductor of the associated differential module $D^{dag}(V)$ defined by Kedlaya in [Ked]. This construction is a generalization to the non perfect residue case of the Fontaines formalism as presented in [Tsu98a]. Our method of proof will allow us to give a new interpretation of the Refined Swan Conductor.
قيم البحث
اقرأ أيضاً
We provide a necessary and sufficient condition for the solvability of a rank one differential (resp. $q$-difference) equation over the Amices ring. We also extend to that ring a Birkoff decomposition result, originally due to Motzkin.
We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications we give a new interpretation of arithmetic Laplacians and we discuss the de Rham cohomology of some specific arithmetic jet spaces.
We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli space. We show
that the set of integral points on any nondegenerate algebraic curve on the moduli space can be effectively determined.
Let $K$ be a field complete with respect to a discrete valuation $v$ of residue characteristic $p$. Let $f(z) in K[z]$ be a separable polynomial of the form $z^ell-c.$ Given $a in K$, we examine the Galois groups and ramification groups of the extens
ions of $K$ generated by the solutions to $f^n(z)=a$. The behavior depends upon $v(c)$, and we find that it shifts dramatically as $v(c)$ crosses a certain value: $0$ in the case $p mid ell$, and $-p/(p-1)$ in the case $p=ell$.
Let $G$ be a connected reductive group over a $p$-adic local field $F$. We propose and study the notions of $G$-$varphi$-modules and $G$-$(varphi, abla)$-modules over the Robba ring, which are exact faithful $F$-linear tensor functors from the catego
ry of $G$-representations on finite-dimensional $F$-vector spaces to the categories of $varphi$-modules and $(varphi, abla)$-modules over the Robba ring, respectively, commuting with the respective fiber functors. We study Kedlayas slope filtration theorem in this context, and show that $G$-$(varphi, abla)$-modules over the Robba ring are $G$-quasi-unipotent, which is a generalization of the $p$-adic local monodromy theorem proven independently by Y. Andre, K. S. Kedlaya, and Z. Mebkhout.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
