Searches , social queries for ADELIC ALGEBRAIC-GROUP
Search references for ADELIC ALGEBRAIC-GROUP. Phrases containing ADELIC ALGEBRAIC-GROUP
See searches and references containing ADELIC ALGEBRAIC-GROUP!
Search references for ADELIC ALGEBRAIC-GROUP. Phrases containing ADELIC ALGEBRAIC-GROUP
See searches and references containing ADELIC ALGEBRAIC-GROUP!ADELIC ALGEBRAIC-GROUP
Semitopological group in abstract algebra
geometry, the adelic points of an algebraic group G {\displaystyle G} over a global field K {\displaystyle K} form a topological group denoted G ( A K
Adelic_algebraic_group
Algebraic variety with a group structure
study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups, including
Algebraic_group
Subgroup of the group of invertible n×n matrices
defined by polynomials, that is, that these are algebraic groups. The founders of the theory of algebraic groups include Maurer, Chevalley, and Kolchin (1948)
Linear_algebraic_group
Concept in mathematics
special orthogonal group SO(n), and the symplectic group Sp(2n). Simple algebraic groups and (more generally) semisimple algebraic groups are reductive. Claude
Reductive_group
Type of generalization of periodic functions in Euclidean space
algebraic group, treated as an adelic algebraic group. It does not completely include the automorphic form idea introduced above, in that the adelic approach
Automorphic_form
Mathematical concept
respect to the induced quotient measure. The Tamagawa measure on the adelic algebraic group G(A) is now defined as follows. Take a left-invariant n-form ω on
Tamagawa_number
Concept in number theory
integrals over adelic groups. More generally, the use of adelic points G ( A K ) {\displaystyle G(\mathbb {A} _{K})} for reductive algebraic groups G {\displaystyle
Adele_ring
Matrix group
integers. Given any algebraic group G {\displaystyle \mathbf {G} } over Q {\displaystyle \mathbb {Q} } the adelic algebraic group G ( A ) {\displaystyle
Congruence_subgroup
Idele group Idele class group Adelic algebraic group Global field Hasse principle Hasse–Minkowski theorem Galois module Galois cohomology Brauer group Class
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Branch of mathematics that studies abstract algebraic structures
dealing with the case that G {\displaystyle G} is an algebraic group, treated as an adelic algebraic group. As a result, an entire philosophy, the Langlands
Representation_theory
Objects extending the notion of functions
compact groups that goes beyond the manifolds that are the typical function domains. The applications are mostly in number theory, particularly to adelic algebraic
Generalized_function
Branch of number theory
Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields
Algebraic_number_theory
Discrete subgroup in a locally compact topological group
and proven for adélic groups rather than for Lie groups. Another group of phenomena concerning lattices in semisimple algebraic groups is collectively
Lattice_(discrete_subgroup)
Mathematical functions that quantify complexity
equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers. For instance, the classical
Height_function
Linear operator acting on modular forms
Hecke operators is by means of double cosets in the modular group. In the contemporary adelic approach, this translates to double cosets with respect to
Hecke_operator
Mathematical Theory
the technique successful. Hervé Jacquet and Robert Langlands later gave adelic integral representations for the standard, and tensor product L-functions
Rankin–Selberg_method
Aspect of algebraic number theory
PlanetMath. Stein, William (2004), A brief introduction to classical and adelic algebraic number theory Neukirch, Jürgen (1999). Algebraische Zahlentheorie.
Splitting of prime ideals in Galois extensions
Splitting_of_prime_ideals_in_Galois_extensions
Concept in number theory
C_{K}=I_{K}/K^{\times }} is a locally compact topological group and a Hausdorff space. More generally, in the adelic algebra setting described below, A × {\displaystyle
Idele_group
Type of vector space
using adelic groups. These play a central role in the Langlands correspondence. The derived Hecke algebra is a further generalization of Hecke algebras to
Hecke_algebra
Mathematic theory
to the general linear group GL(n, k) over an algebraic number field k, and to automorphic representations of its adelic group, which formed the foundations
Tate's_thesis
Book about number theory
book is modern in its consistent use of adelic and idèlic methods and the simultaneous treatment of algebraic number fields and rational function fields
Basic_Number_Theory
French mathematician (1906-1998)
conjecture on Tamagawa numbers proved resistant for many years. Eventually the adelic approach became basic in automorphic representation theory. He picked up
André_Weil
functions; these representations may be of adelic algebraic groups. When the group is the general linear group GL 2 {\displaystyle \operatorname {GL} _{2}}
Cuspidal_representation
Mathematical law, a generalization of quadratic reciprocity
reciprocity laws using cohomology of groups or representations of adelic groups or algebraic K-groups, and their relationship with the original quadratic reciprocity
Reciprocity_law
Mathematical theory
theory P-adic Hodge theory Adelic group Leong, Y. K. (July–December 2018). "Shou-Wu Zhang: Number Theory and Arithmetic Algebraic Geometry" (PDF). Imprints
Arakelov_theory
Chinese mathematician (born 1981)
Ullmo and Shou-Wu Zhang to the broader framework of adelic line bundles and in particular to algebraic dynamical systems. Together with Shou-Wu Zhang, Yuan
Xinyi_Yuan
Russian mathematician (1942–2022)
Parshin, A. N.; Shafarevich, I. R., eds. (1994). Algebraic Geometry IV – Linear Algebraic Groups Invariant Theory. Encyclopaedia of Mathematical Sciences
Aleksei_Parshin
Concept in algebraic geometry
Grothendieck Approaches to Adelic Points" (PDF). Archived (PDF) from the original on 21 July 2018. Neukirch, Jürgen (1999). "1.13". Algebraic Number Theory. Berlin
Noetherian_scheme
British mathematician and logician
leading figure in model theory, logic, and their applications in algebra, algebraic geometry, and number theory. He is Emeritus Professor of Mathematics
Angus_Macintyre
Structure in algebraic geometry
In algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes
Nisnevich_topology
American mathematician
, vol. 103, 2011, pp. 197–234. ArXiv with Dragoș Ghioca: Algebraic equations on the adèlic closure of a Drinfeld module. In: Israel J. Math., vol. 194
Thomas_W._Scanlon
Canadian mathematician
for quaternion algebras. This book applied the adelic trace formula for G L ( 2 ) {\displaystyle \mathrm {GL} (2)} and quaternion algebras to do this. Subsequently
Robert_Langlands
locaux et isogenies (isogeny) André Weil, Adèles et groupes algébriques (adelic algebraic groups) Jacques Deny, Formes et espaces de Dirichlet (Dirichlet
Séminaire Nicolas Bourbaki (1950–1959)
Séminaire_Nicolas_Bourbaki_(1950–1959)
Type of zeta function
L-functions". Arithmetical Algebraic Geometry, Proc. Conf. Purdue Univ. 1963. Harper and Row. John Tate (1965). "Algebraic cycles and poles of zeta functions"
Arithmetic_zeta_function
Mathematical theorem
representation theory of an adelic reductive algebraic group. The multiplicity in question is the number of times a given abstract group representation is realised
Multiplicity-one_theorem
Mathematical theorem
for algebraic groups over the adeles rather than for Lie groups, because this makes the corresponding discrete subgroup Γ into an algebraic group over
Selberg_trace_formula
subgroup Γ of a real Lie group G(R) (usually SL2(R)). In higher rank it is more convenient to replace the Lie group with an adelic group G(A). One reason for
Arthur–Selberg_trace_formula
{\displaystyle \mathbf {R} } . In algebraic number theory, the Schwartz–Bruhat functions on the adeles can be used to give an adelic version of the Poisson summation
Schwartz–Bruhat_function
Functions on special groups related to their matrix representations
automorphic representations of adelic groups. This approach was further developed by Langlands, for general reductive algebraic groups over global fields. Peter–Weyl
Matrix_coefficient
Australian mathematician
George A. (2013). "Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity". Geometric and Functional Analysis. 23 (5):
George_A._Willis
Mathematical concept
(2005), who derived the explicit formula of Weil via harmonic analysis on adelic spaces. Selberg trace formula Selberg zeta function The original prime counting
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
Graduate-level textbooks in mathematics
Volume Title Author(s) Publication Date Pages ISBN/LCCN 1 Algebraic Theory of Numbers Hermann Weyl 1940 223 LCCN 40-13494 2 Convergence and Uniformity
Annals_of_Mathematics_Studies
conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin–Mumford conjecture in arithmetic geometry
Bogomolov_conjecture
French mathematician (born 1953)
components of the spaces of square-integrable invariant functions on adelic general linear groups.[MW89] For this purpose it was first necessary to write down
Colette_Moeglin
travel, tourism, insurance
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
ADELIC ALGEBRAIC-GROUP
travel, tourism, insurance