About: Tamagawa number

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In mathematics, the Tamagawa number of a semisimple algebraic group defined over a global field k is the measure of , where is the adele ring of k. Tamagawa numbers were introduced by Tamagawa, and named after him by Weil.

Attributes	Values
rdf:type	Thing
rdfs:label	Tamagawa number (en)
rdfs:comment	In mathematics, the Tamagawa number of a semisimple algebraic group defined over a global field k is the measure of , where is the adele ring of k. Tamagawa numbers were introduced by Tamagawa, and named after him by Weil. (en)
rdfs:seeAlso	Weil conjecture on Tamagawa numbers
dcterms:subject	Algebraic groups Algebraic number theory
Wikipage page ID	1168653 (xsd:integer)
Wikipage revision ID	1047610863 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebraic function field Algebraic group Annals of Mathematics Algebraic groups Mathematics Classical group Dennis Gaitsgory Adele ring Adelic algebraic group Undefined (mathematics) Haar measure Semisimple algebraic group American Mathematical Society Dimension of an algebraic variety Global field Quadratic form Jacob Lurie Algebraic number theory Tsuneo Tamagawa Differential form Completion (algebra) Weil's conjecture on Tamagawa numbers Semisimple group
Link from a Wikipage to an external page	https://www.cornell.edu/video/jacob-lurie-the-siegel-mass-formula https://arxiv.org/abs/0801.4733 https://books.google.com/books%3Fid=vQvvAAAAMAAJ http://www.numdam.org/item%3Fid=SB_1958-1960__5__249_0 http://www.math.harvard.edu/~lurie/282y.html
sameAs	Tamagawa number Tamagawa number
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Harvtxt dbt:Math dbt:See_also dbt:Sfn dbt:Harvs
id	T/t092060 (en)
title	Tamagawa number (en)
has abstract	In mathematics, the Tamagawa number of a semisimple algebraic group defined over a global field k is the measure of , where is the adele ring of k. Tamagawa numbers were introduced by Tamagawa, and named after him by Weil. Tsuneo Tamagawa's observation was that, starting from an invariant differential form ω on G, defined over k, the measure involved was well-defined: while ω could be replaced by cω with c a non-zero element of , the product formula for valuations in k is reflected by the independence from c of the measure of the quotient, for the product measure constructed from ω on each effective factor. The computation of Tamagawa numbers for semisimple groups contains important parts of classical quadratic form theory. (en)
prov:wasDerivedFrom	wikipedia-en:Tamagawa_number?oldid=1047610863&ns=0
page length (characters) of wiki page	6264 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Tamagawa_number
is Link from a Wikipage to another Wikipage of	Basel problem Birch and Swinnerton-Dyer conjecture Special values of L-functions Glossary of arithmetic and diophantine geometry 1 Algebraic number theory Tsuneo Tamagawa Smith–Minkowski–Siegel mass formula Weil's conjecture on Tamagawa numbers Weil conjecture
is foaf:primaryTopic of	wikipedia-en:Tamagawa_number

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