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Let $p$ be a rational prime and $K$ a complete discrete valuation field with residue field $k$ of positive characteristic $p$ . When $k$ is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local $ε_{0}$ -constants for representations, over a complete local ring with an algebraically closed residue field of characteristic $\neq p$ , of the Weil group $W_{K}$ of $K$ . In this paper, we generalize the results in [10] and [11] to the case where $k$ is an arbitrary perfect field.

Local-global compatibility for $l = p$ , I

Thomas Barnet-Lamb, Toby Gee, David Geraghty, Richard Taylor (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the compatibility of the local and global Langlands correspondences at places dividing $l$ for the $l$ -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of ${GL}_{n}$ over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing $l$ and have Shin-regular weight.

Local-global principle for certain biquadratic normic bundles

Yang Cao, Yongqi Liang (2014)

Acta Arithmetica

Let X be a proper smooth variety having an affine open subset defined by the normic equation $N_{k (\sqrt a, \sqrt b) / k} (x) = Q (t ₁, . . ., t ₘ) ²$ over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.

Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains

Yong HU (2012)

Annales de l’institut Fourier

Let $R$ be a 2-dimensional normal excellent henselian local domain in which $2$ is invertible and let $L$ and $k$ be its fraction field and residue field respectively. Let $Ω_{R}$ be the set of rank 1 discrete valuations of $L$ corresponding to codimension 1 points of regular proper models of $Spec R$ . We prove that a quadratic form $q$ over $L$ satisfies the local-global principle with respect to $Ω_{R}$ in the following two cases: (1) $q$ has rank 3 or 4; (2) $q$ has rank $\geq 5$ and $R = A [[y]]$ , where $A$ is a complete discrete valuation ring with...

Local-global principle for Witt equivalence of function fields over global fields

Przemyslaw Koprowski (2002)

Colloquium Mathematicae

We examine the conditions for two algebraic function fields over global fields to be Witt equivalent. We develop a criterion solving the problem which is analogous to the local-global principle for Witt equivalence of global fields obtained by R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland [12]. Subsequently, we derive some immediate consequences of this result. In particular we show that Witt equivalence of algebraic function fields (that have rational places) over global fields implies...

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Local L-factors of motives and regularized determinants.

Local p-dimensional Galois characters.

Local problems with primes I.

Local relation of Gauss sums

Local return rates in Sturmian subshifts

Local Root Numbers and Hermitian Â? Galois Module Structure of Rings of Integers.

Local Shimura Correspondence.

Local solvability of diagonal equations (again)

Local tame lifting for $G L (N)$ . I: Simple characters

Local units, elliptic units, Heegner points and elliptic curves.

Local $ε_{0}$ -characters in torsion rings

Local-global compatibility for $l = p$ , I

Local-global principle for certain biquadratic normic bundles

Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains

Local-global principle for Witt equivalence of function fields over global fields

Localisation de formes quadratiques $I$

Localisation de formes quadratiques. II

Localised Bombieri-Vinogradov theorems in imaginary quadratic fields

Localised value-distribution of additive arithmetic functions.

Localization of the cohomology of a finite galois group in a Dedekind domain

Currently displaying 341 – 360 of 460