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In mathematics, a Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in such a way that the ring of Witt vectors over the finite field of order is the ring of -adic integers. They have a highly non-intuitive structure upon first glance because their additive and multiplicative structure depends on an infinite set of recursive formulas which do not behave like addition and multiplication formulas for standard p-adic integers. The main idea behind Witt vectors is instead of using the standard -adic expansion

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Group100031264 yago:WikicatAlgebraicGroups
rdfs:label	Wittvektor (de) Vecteur de Witt (fr) 비트 벡터 (ko) Pierścień Witta (pl) Witt vector (en) Вектор Витта (ru)
rdfs:comment	Wittvektoren sind eine von dem Mathematiker Ernst Witt eingeführte Verallgemeinerung der Konstruktion der (ganzen) p-adischen Zahlen auf beliebige perfekte Restklassenkörper. Neben diesen -typischen Wittvektoren gibt es die großen Wittvektoren, aus denen sich die -typischen Wittvektoren für beliebiges rekonstruieren lassen. (de) Les vecteurs de Witt sont des objets mathématiques, généralement décrits comme des suites infinies de nombres (ou plus généralement d'éléments d'un anneau). Ils ont été introduits par Ernst Witt en 1936, afin de décrire les extensions non ramifiées des corps de nombres p-adiques. Ces vecteurs sont dotés d'une structure d'anneau ; on parle donc de l’anneau des vecteurs de Witt. Ils apparaissent aujourd'hui dans plusieurs branches de la géométrie algébrique et arithmétique, en théorie des groupes et en physique théorique. (fr) 가환대수학에서 비트 벡터 환(Witt vector環, 영어: ring of Witt vectors)은 주어진 가환환 속의 열들의 집합 위에 줄 수 있는 특별한 가환환 구조이다. p진 정수환의 일반화이다. (ko) Pierścień Witta – pierścień o strukturze przekształconej w zbiór wektorów w taki sposób, że pierścień wektorów nad skończonym ciałem o charakterystyce jest pierścieniem liczb p-adycznych. Nazwa pochodzi od Ernsta Witta, który jako pierwszy dokonał takiego przekształcenia. (pl) In mathematics, a Witt vector is an infinite sequence of elements of a commutative ring. Ernst Witt showed how to put a ring structure on the set of Witt vectors, in such a way that the ring of Witt vectors over the finite field of order is the ring of -adic integers. They have a highly non-intuitive structure upon first glance because their additive and multiplicative structure depends on an infinite set of recursive formulas which do not behave like addition and multiplication formulas for standard p-adic integers. The main idea behind Witt vectors is instead of using the standard -adic expansion (en) В математике вектором Витта называется бесконечная последовательность элементов коммутативного кольца. Эрнст Витт (нем. Ernst Witt) показал, как наложить структуру кольца на множество векторов Витта таким образом, что кольцо векторов Витта над конечным полем порядка p является кольцом p-адических целых. (ru)
dcterms:subject	Combinatorics on words Algebraic groups Ring theory
Wikipage page ID	5573710 (xsd:integer)
Wikipage revision ID	1115603228 (xsd:integer)
Link from a Wikipage to another Wikipage	Power series Princeton University Press Root of unity Ring of symmetric functions Binomial coefficient Binomial coefficients Algebraic group Algebraic number field Algebraically closed field Combinatorics on words Algebraic groups Ring theory Mathematics Fully faithful functor Necklace ring André Joyal Commutative ring Functor Kummer theory Mathematical structure Logarithmic derivative Abraham Adrian Albert Affine space Ernst Witt Fermat's Last Theorem Finite field Formal power series Oswald Teichmüller P-adic integer P-adic number Forgetful functor Formal criteria for adjoint functors Projection (mathematics) Inverse limit Isogeny Prime number Accessible category Least common multiple Teichmüller character Artin–Hasse exponential Artin–Schreier theory Free object Kurt Hensel Newton's method Category (mathematics) Real closed field Morphism of schemes Unipotent Formal group Splitting of prime ideals in Galois extensions Perfect field P-derivation Ernst Eduard Kummer Frobenius homomorphism Right adjoint Springer-Verlag P-adic metric Artin–Schreier theorem Infinite sequence Hensel lifting dbr:Arxiv:1409.7445
Link from a Wikipage to an external page	https://archive.org/details/algebraicgroupsc0000serr http://www.digizeitschriften.de/main/dms/img/%3FIDDOC=504725 https://web.archive.org/web/20190112130142/http:/www.claymath.org/sites/default/files/brinon_witt.pdf http://www.numdam.org/item/ASENS_1979_4_12_4_501_0/
sameAs	Witt vector Witt vector Witt vector Witt vector Witt vector Witt vector Witt vector Witt vector Witt vector
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Cite_book dbt:Reflist
authorlink	Igor Dolgachev (en)
first	Igor V. (en)

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