Linear algebraic groups with good reduction (Q2221525)

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Language	Label	Description	Also known as
English	Linear algebraic groups with good reduction	scientific article

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scholarly article

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Linear algebraic groups with good reduction (English)

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Igor A. Rapinchuk

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Andrei S. Rapinchuk

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Research in the Mathematical Sciences

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publication date

2 February 2021

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full work available at URL

https://arxiv.org/abs/2005.05484

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MaRDI profile type

MaRDI publication profile

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Generic splitting fields of central simple algebras

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\(K\)-theory and stable algebra

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Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)

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Examples of algebraic groups of type \(G_2\) having the same maximal tori

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Some finiteness properties of adele groups over number fields

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Théoremes de finitude en cohomologie galoisienne

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Homomorphismes ''abstraits'' de groupes algébriques simples

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On abstract representations of the groups of rational points of algebraic groups in positive characteristic

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Torsors over the punctured affine line

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On conjugacy of Cartan subalgebras in extended affine Lie algebras

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The genus of a division algebra and the unramified Brauer group

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Division algebras with the same maximal subfields

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On the size of the genus of a division algebra

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On some finiteness properties of algebraic groups over finitely generated fields

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Spinor groups with good reduction

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The finiteness of the genus of a finite-dimensional division algebra, and some generalizations

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Some finiteness results for the group \(SK_1\) of a biquaternion algebra

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Patching and local-global principles for homogeneous spaces over function fields of \(p\)-adic curves

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Fibres quadratiques et composantes connexes réelles

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Finiteness theorems for algebraic groups over function fields

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Pseudo-reductive Groups

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Introduction to Algebraic Geometry

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Schémas en groupes. I: Propriétés générales des schémas en groupes. Exposés I à VIIb. Séminaire de Géométrie Algébrique 1962/64, dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint

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Finiteness theorems for abelian varieties over number fields.

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There are no abelian varieties over \(\mathbb Z\).

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Outer automorphisms of algebraic groups and determining groups by their maximal tori.

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Quaternion Algebras with the Same Subfields

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Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C.

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Torsors on the affine line

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Isotriviality and étale cohomology of Laurent polynomial rings

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Groups over \(\mathbb{Z}\)

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Smallness of fundamental groups for arithmetic schemes

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Applications of patching to quadratic forms and central simple algebras

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Local-global principles for torsors over arithmetic curves

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Halbeinfache Gruppenschemata über Dedekindringen

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Über die Galoiskohomologie halbeinfacher algebraischer Gruppen. III.

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Motivic equivalence of quadratic forms

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Hasse principles for higher-dimensional fields

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Good reduction of algebraic groups and flag varieties

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Can One Hear the Shape of a Drum?

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Sur le groupe des classes d’un schéma arithmétique

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Criteria of motivic equivalence for quadratic forms and central simple algebras

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A Hasse principle for two dimensional global fields.

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Starke Approximation in algebraischen Gruppen. I.

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Théorie de la descente et algèbres d'Azumaya

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Distinguishing division algebras by finite splitting fields.

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Division algebras with infinite genus

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Introduction to Algebraic K-Theory. (AM-72)

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An exact sequence for \(K^M_*/2\) with applications to quadratic forms

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A Hasse principle for quadratic forms over function fields

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Reduced K-theory and approximation in algebraic groups

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Strong approximation for semi-simple groups over function fields

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Weakly commensurable arithmetic groups and isospectral locally symmetric spaces

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Local-global principles for embedding of fields with involution into simple algebras with involution

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On the fields generated by the lengths of closed geodesics in locally symmetric spaces

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Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces

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Principal bundles on the affine line

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On strong approximation for algebraic groups

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On division algebras having the same maximal subfields.

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On linear representations of Chevalley groups over commutative rings

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On abstract representations of the groups of rational points of algebraic groups and their deformations.

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On the character varieties of finitely generated groups.

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On abstract homomorphisms of Chevalley groups over the coordinate rings of affine curves

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A generalization of Serre's condition (F) with applications to the finiteness of unramified cohomology

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Isospectrality and commensurability of arithmetic hyperbolic 2- and 3- manifolds

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Anneaux gradués factoriels et modules réflexifs

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Le problème des groupes de congruence pour \(SL_2\)

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Profinite Groups, Arithmetic, and Geometry. (AM-67)

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On semisimple representations of universal lattices.

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The Arithmetic of Elliptic Curves

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Rational Points on Elliptic Curves

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Linear algebraic groups.

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Chevalley groups of polynomial rings over Dedekind domains

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ON THE STRUCTURE OF THE SPECIAL LINEAR GROUP OVER POLYNOMIAL RINGS

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Galois Groups and Fundamental Groups

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Division algebras of prime degree with infinite genus

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Free subgroups in linear groups

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RINGS OF DEFINITION OF DENSE SUBGROUPS OF SEMISIMPLE LINEAR GROUPS

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Strong approximation theorem for division algebras over \(\mathbb{R}(X)\)

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Identifiers

zbMATH Open document ID

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10.1007/s40687-020-00226-3

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2221525

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