Related papers: Hasse principle for hermitian spaces over semi-glo…
This paper aims at developing a "local--global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the…
We establish the Hasse principle (local-global principle) in the context of the Baum-Connes conjecture with coefficients. We illustrate this principle with the discrete group $GL(2,F)$ where $F$ is any global field.
Let $C$ be a smooth projective curve defined over the finite field $\mathbb{F}_q$ ($q$ is odd) and let $K=\mathbb{F}_q(C)$ be its function field. Removing one closed point $C^\text{af} = C-\{\infty\}$ results in an integral domain…
The aim of this note is to revisit the question of local-global principles for embeddings of etale algebras with involution into central simple algebras with involution over global fields of characteristic not 2. A necessary and sufficient…
We prove a local-global principle for torsors under the prosolvable geometric fundamental group of a hyperbolic curve over a number field.
Nous montrons, pour une grande famille de propri\'et\'es $P$ des espaces homog\`enes, que $P$ vaut pour tout espace homog\`ene d'un groupe lin\'eaire connexe d\`es qu'elle vaut pour les espaces homog\`enes de $\mathrm{SL}_n$ \`a…
This paper provides applications of patching to quadratic forms and central simple algebras over function fields of curves over henselian valued fields. In particular, we use a patching approach to reprove and generalize a recent result of…
A finite extension of global fields $L/K$ satisfies the Hasse norm principle if any nonzero element of $K$ has the property that it is a norm locally if and only if it is a norm globally. In 1931, Hasse proved that any cyclic extension…
K. Kato's conjecture about the cohomological Hasse principle for regular connected schemes $\mathfrak X$ which are flat and proper over the complete discrete valuation rings $\mathcal O_N$ of higher local fields $F_N$ is proven. This…
The Hasse principle in number theory states that information about integral solutions to Diophantine equations can be pieced together from real solutions and solutions modulo prime powers. We show that the Hasse principle holds for…
Lichtenbaum proved that index and period coincide for a curve of genus one over a $p$-adic field. Salberger proved that the Hasse principle holds for a smooth complete intersection of two quadrics $X \subset P^n$ over a number field, if it…
In this paper we deduce a graded version of Quillen--Suslin's Local-Global Principle for the traditional classical groups, viz. general linear, symplectic and orthogonal groups and establish its equivalence of the normality property of the…
Let $R$ be the henselization of a local ring of a semistable family over the spectrum of a discrete valuation ring of mixed characteristic $(0, p)$ and $k$ the residue field of $R$. In this paper, we prove an isomorphism of \'{e}tale…
We investigate the Hasse principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets of discrete valuations. Over purely transcendental field extensions of fields that…
In this paper we prove local-global principles for embedding of fields with involution into central simple algebras with involution over a global field. These should be of interest in study of classical groups over global fields. We deduce…
We prove a local-global principle for torsors under the prosolvable geometric fundamental group of an affine curve over a number field.
Let k be a global field. Let G be a connected linear algebraic k-group, assumed reductive when k is a function field. It follows from a result of a preprint by Bary-Soroker, Fehm and Petersen that when H is a smooth connected k-subgroup of…
Asymptotic Schur orthogonality relations are for irreducible unitary representations of locally compact groups that need not be discrete series, where $L^2$ pairing of matrix coefficients with respect to Haar measure is replaced by a limit…
Let $R$ be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an $R$-algebra with involution, which are rationally ismorphic and have isomorphic semisimple coradicals,…
In this article we extend the validity Suslin's Local-Global Principle for the elementary transvection subgroup of the general linear group, the symplectic group, and the orthogonal group, where n > 2, to a Local-Global Principle for the…