We show that the completed Hecke algebra of $p$ -adic modular forms is isomorphic to continuous automorphic for units quaternion ramified at and $\infty$ . This gives an affirmative answer a question posed by Serre in 1987 letter Tate. The proof geometric, lifts mod argument due Serre: we evaluate identifying quaternionic double-coset with fiber Hodge–Tate period map, extend functions off using...

We continue our study of the general notion of L-Chu correspondence by introducing the category CRL-ChuCors incorporating residuation to the underlying complete lattice L, specifically, on the basis of a residuation-preserving isotone Galois connection λ. Then, the L-bonds are generalized within this same framework, and its structure is related to that of the extent of a suitably defined λ-dire...

Let F be a non-Archimedean local field with finite residual field of characteristic p. In this article we calculate the ε-factor of pairs for GLl(F ) ×GLl′(F ) where l and l are distinct primes including the case l = p. For this calculation, we use the local Langlands correspondence and non-Galois base change lift. This method leads to the explicit conjecture of the ε-factor of the representati...

Valuations on a field K are encoded in the absolute Galois group GK of K: They are in one-to-one correspondence to the conjugacy classes of decomposition subgroups of GK which (apart from few exceptions) can be characterized in group theoretic terms. Roughly speaking decomposition subgroups of GK are maximal subgroups of GK with a Sylow-subgroup containing a non-trivial abelian normal subgroup....

We prove that if a conditional expectation from a simple C∗-algebra onto its C∗-subalgebra satisfies the Pimsner-Popa inequality, there exists a quasibasis. As an application, we establish the Galois correspondence for outer actions of finite groups (and more generally finite dimensional Kac algebras) on simple C∗algebras. We also introduce the notion of sectors for stable simple C∗-algebras an...

We establish integral analogues of results of Bushnell and Henniart [BH] for spaces of Whittaker functions arising from the groups GLn(F ) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the conjectural “local Langlands correspondence in families” of [EH], and reduce the question of the existence of such representations to a natural conjectur...

In this paper, we establish Galois theory for partial differential systems defined over formally real fields with a closed field of constants and $p$-adic $p$-adically constants. For an integrable system such field, prove that there exists (resp. $p$-adic) Picard-Vessiot extension. Moreover, obtain uniqueness result We give adequate definition the group fundamental theorem in setting. apply obt...

Twenty-five years ago R. Langlands proposed [L] a “fantastic generalization” of Artin-Hasse reciprocity law in the classical class field theory. He conjectured the existence of a correspondence between automorphic irreducible infinite-dimensional representations of a reductive groupG over a global number field on the one hand, and (roughly speaking) finite dimensionsional representations of the...

We generalize the notion of complete binary relation on complete lattice to residuated lattice valued ordered sets and show its properties. Then we focus on complete fuzzy tolerances on fuzzy complete lattices and prove they are in one-to-one correspondence with extensive isotone Galois connections. Finally, we prove that fuzzy complete lattice, factorized by a complete fuzzy tolerance, is agai...