اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPersitence of non degeneracy: a local analog of Iharas lemma
50
0
0.0
(
0
)
تأليف
Pascal Boyer
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Persitence of non degeneracy is a phenomenon which appears in the theory of $overline{mathbb Q}_l$-representations of the linear group: every irreducible submodule of the restriction to the mirabolic subgroup of an non degenerate irreducible representation is non degenerate. This is no more true in general, if we look at the modulo $l$ reduction of some stable lattice. As in the Clozel-Harris-Taylor generalization of global Iharas lemma, we show that this property, called non degeneracy persitence, remains true for lattices given by the cohomology of Lubin-Tate spaces.
قيم البحث
اقرأ أيضاً
A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Iharas lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate, Clozel-Harris-Taylor proposed
a generalization of the Iharas lemma in higher dimension for some similitude groups. The main aim of this paper is then to prove some new instances of this generalized Iharas lemma by considering some particular non pseudo Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level rising statement.
We exhibit cases of a level fixing phenomenon for galoisian automorphic representations of a CM field $F$, with dimension $d geq 2$. The proof rests on the freeness of the localized cohomology groups of KHT Shimura varieties and the strictness of its
filtration induced by the spectral sequence associated to the filtration of stratification of the nearby cycles perverse sheaf at some fixed place $v$ of $F$. The main point is the observation that the action of the unipotent monodromy operator at $v$ is then given by those on the nearby cycles where its order of nilpotency modulo $l$ equals those in characteristic zero. Finally we infer some consequences concerning level raising and Iharas lemma.
We consider a large family of integro-differential equations and establish a non-local counterpart of Hopfs lemma, directly expressed in terms of the symbol of the operator. As closely related problems, we also obtain a variety of maximum principles
for viscosity solutions. In our approach we combine direct analysis with functional integration, allowing a robust control around the boundary of the domain, and make use of the related ascending ladder height-processes. We then apply these results to a study of principal eigenvalue problems, the radial symmetry of the positive solutions, and the overdetermined non-local torsion equation.
By Mazurs Torsion Theorem, there are fourteen possibilities for the non-trivial torsion subgroup $T$ of a rational elliptic curve. For each $T$, we consider a parameterized family $E_T$ of elliptic curves with the property that they parameterize all
elliptic curves $E/mathbb{Q}$ which contain $T$ in their torsion subgroup. Using these parameterized families, we explicitly classify the N{e}ron type, the conductor exponent, and the local Tamagawa number at each prime $p$ where $E/mathbb{Q}$ has additive reduction. As a consequence, we find all rational elliptic curves with a $2$-torsion or a $3$-torsion point that have global Tamagawa number~$1$.
We develop a framework for the rigorous analysis of focused stochastic local search algorithms. These are algorithms that search a state space by repeatedly selecting some constraint that is violated in the current state and moving to a random nearby
state that addresses the violation, while hopefully not introducing many new ones. An important class of focused local search algorithms with provable performance guarantees has recently arisen from algorithmizations of the Lov{a}sz Local Lemma (LLL), a non-constructive tool for proving the existence of satisfying states by introducing a background measure on the state space. While powerful, the state transitions of algorithms in this class must be, in a precise sense, perfectly compatible with the background measure. In many applications this is a very restrictive requirement and one needs to step outside the class. Here we introduce the notion of emph{measure distortion} and develop a framework for analyzing arbitrary focused stochastic local search algorithms, recovering LLL algorithmizations as the special case of no distortion. Our framework takes as input an arbitrary such algorithm and an arbitrary probability measure and shows how to use the measure as a yardstick of algorithmic progress, even for algorithms designed independently of the measure.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
