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기하학 수리물리 연구단
기하학 수리물리 연구단
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Witt vectors as a polynomial functor

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Title
Witt vectors as a polynomial functor
Author(s)
D. Kaledin
Publication Date
2018-03
Journal
SELECTA MATHEMATICA-NEW SERIES, v.24, no.1, pp.359 - 402
Publisher
SPRINGER BASEL AG
Abstract
For every commutative ring A, one has a functorial commutative ring W(A) of p-typical Witt vectors of A, an iterated extension of A by itself. If A is not commutative, it has been known since the pioneering work of L. Hesselholt that W(A) is only an abelian group, not a ring, and it is an iterated extension of the Hochschild homology group by itself. It is natural to expect that this construction generalizes to higher degrees and arbitrary coefficients, so that one can define "Hochschild-Witt homology" for any bimodule M over an associative algebra A over a field k. Moreover, if one want the resulting theory to be a trace theory, then it suffices to define it for . This is what we do in this paper, for a perfect field k of positive characteristic p. Namely, we construct a sequence of polynomial functors , from k-vector spaces to abelian groups, related by restriction maps, we prove their basic properties such as the existence of Frobenius and Verschiebung maps, and we show that are trace functors. The construction is very simple, and it only depends on elementary properties of finite cyclic groups. © Springer International Publishing AG 2017
URI
https://pr.ibs.re.kr/handle/8788114/6491
ISSN
1022-1824
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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