Results 11 to 20 of about 104,032 (100)
Linearizing torsion classes in the Picard group of algebraic curves over finite fields
Journal of Algebra, 2009 We address the problem of computing in the group of $\ell^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.
openaire +4 more sources
A lattice in more than two Kac--Moody groups is arithmetic
, 2008 Let $\Gamma$ be an irreducible lattice in a product of n infinite irreducible complete Kac-Moody groups of simply laced type over finite fields. We show that if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic group over a local ...
A. Borel +36 more
core +1 more source
, 2017 The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families.
Wedhorn, Torsten
core +3 more sources
Homomorphic encryption and some black box attacks
, 2020 This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic encryption schemes ...
A Acar +10 more
core +1 more source
Hecke algebra isomorphisms and adelic points on algebraic groups [PDF]
, 2015 Let $G$ denote a linear algebraic group over $\mathbf{Q}$ and $K$ and $L$ two number fields. Assume that there is a group isomorphism of points on $G$ over the finite adeles of $K$ and $L$, respectively.
Cornelissen, Gunther +1 more
core
Grothendieck's theorem on non-abelian H^2 and local-global principles
, 1998 A theorem of Grothendieck asserts that over a perfect field k of cohomological dimension one, all non-abelian H^2-cohomology sets of algebraic groups are trivial.
Flicker, Yuval Z. +2 more
core +1 more source
Geometry of word equations in simple algebraic groups over special fields
, 2018 This paper contains a survey of recent developments in investigation of word equations in simple matrix groups and polynomial equations in simple (associative and Lie) matrix algebras along with some new results on the image of word maps on algebraic ...
Gordeev, Nikolai +2 more
core +1 more source
Khronos, 2016 This paper stresses a specific line of development of the notion of finite field, from Évariste Galois’s 1830 “Note sur la théorie des nombres,” and Camille Jordan’s 1870 Traité des substitutions et des équations algébriques, to Leonard Dickson’s 1901 ...
Frédéric BRECHENMACHER
doaj
How to use finite fields for problems concerning infinite fields
, 2009 The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.Comment: 12 ...
Serre, Jean-Pierre
core +1 more source
Approximate subgroups of linear groups
, 2010 We establish various results on the structure of approximate subgroups in linear groups such as SL_n(k) that were previously announced by the authors. For example, generalising a result of Helfgott (who handled the cases n = 2 and 3), we show that any ...
Breuillard, Emmanuel +2 more
core +1 more source