اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUnramifiedness of Galois representations arising from Hilbert modular surfaces
128
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $p$ be a prime number and $F$ a totally real number field. For each prime $mathfrak{p}$ of $F$ above $p$ we construct a Hecke operator $T_mathfrak{p}$ acting on $(mathrm{mod}, p^m)$ Katz Hilbert modular classes which agrees with the classical Hecke operator at $mathfrak{p}$ for global sections that lift to characteristic zero. Using these operators and the techniques of patching complexes of F. Calegari and D. Geraghty we prove that the Galois representations arising from torsion Hilbert modular classes of parallel weight ${bf 1}$ are unramified at $p$ when $[F:mathbb Q]=2$. Some partial and some conjectural results are obtained when $[F:mathbb Q]>2$.
قيم البحث
اقرأ أيضاً
In this paper we explicitly compute mod-l Galois representations associated to modular forms. To be precise, we look at cases with l<=23 and the modular forms considered will be cusp forms of level 1 and weight up to 22. We present the result in term
s of polynomials associated to the projectivised representations. As an application, we will improve a known result on Lehmers non-vanishing conjecture for Ramanujans tau function.
In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian variety. Assume that there exists a prime p such that J(C) has semista
ble reduction with toric dimension 1 at p. We provide an algorithm to compute a list of primes l (if they exist) such that the Galois representation attached to the l-torsion of J(C) is surjective onto the group GSp(2n, l). In particular we realize GSp(6, l) as a Galois group over Q for all primes l in [11, 500000].
A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are carefully chosen, they provide compatible systems of Galoi
s representations satisfying some desired properties, e.g. properties that reflect on the image of the members of the system. In this article we survey some results obtained using this strategy.
This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the projectivi
sation of a given symplectic group representation satisfying some natural conditions can be defined. The answer only depends on inner twists. We apply this to the residual representations of a compatible system of symplectic Galois representations satisfying some mild hypothesis and obtain precise information on their projective images for almost all members of the system, under the assumption of huge residual images, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. Finally, we obtain an application to the inverse Galois problem.
Let $mathcal{G}$ be a connected reductive almost simple group over the Witt ring $W(mathbb{F})$ for $mathbb{F}$ a finite field of characteristic $p$. Let $R$ and $R$ be complete noetherian local $W(mathbb{F})$ -algebras with residue field $mathbb{F}$
. Under a mild condition on $p$ in relation to structural constants of $mathcal{G}$, we show the following results: (1) Every closed subgroup $H$ of $mathcal{G}(R)$ with full residual image $mathcal{G}(mathbb{F})$ is a conjugate of a group $mathcal{G}(A)$ for $Asubset R$ a closed subring that is local and has residue field $mathbb{F}$ . (2) Every surjective homomorphism $mathcal{G}(R)tomathcal{G}(R)$ is, up to conjugation, induced from a ring homomorphism $Rto R$. (3) The identity map on $mathcal{G}(R)$ represents the universal deformation of the representation of the profinite group $mathcal{G}(R)$ given by the reduction map $mathcal{G}(R)tomathcal{G}(mathbb{F})$. This generalizes results of Dorobisz and Eardley-Manoharmayum and of Manoharmayum, and in addition provides an abstract classification result for closed subgroups of $mathcal{G}(R)$ with residually full image. We provide an axiomatic framework to study this type of question, also for slightly more general $mathcal{G}$, and we study in the case at hand in great detail what conditions on $mathbb{F}$ or on $p$ in relation to $mathcal{G}$ are necessary for the above results to hold.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
