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Summer 2020 Witt–Burnside functor attached to $\boldsymbol{Z}_{p}^{2}$ and $p$-adic Lipschitz continuous functions
Lance Edward Miller, Benjamin Steinhurst
J. Commut. Algebra 12(2): 263-291 (Summer 2020). DOI: 10.1216/jca.2020.12.263

Abstract

Dress and Siebeneicher gave a significant generalization of the construction of Witt vectors, by producing for any profinite group G , a ring-valued functor W G . This paper gives the first concrete interpretation of any Witt–Burnside rings outside the procyclic cases in terms of known rings. In particular, the rings W Z p 2 ( k ) , where k is a field of characteristic p > 0 have a quotient realized as rings of Lipschitz continuous functions on the p -adic upper half plane P 1 ( Q p ) . As a consequence we show that the Krull dimensions of the rings W Z p d ( k ) are infinite for d 2 and we show the Teichmüller representatives form an analogue of the van der Put basis for continuous functions on Z p .

Citation

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Lance Edward Miller. Benjamin Steinhurst. "Witt–Burnside functor attached to $\boldsymbol{Z}_{p}^{2}$ and $p$-adic Lipschitz continuous functions." J. Commut. Algebra 12 (2) 263 - 291, Summer 2020. https://doi.org/10.1216/jca.2020.12.263

Information

Received: 7 September 2016; Revised: 25 July 2017; Accepted: 31 July 2017; Published: Summer 2020
First available in Project Euclid: 2 June 2020

zbMATH: 07211338
MathSciNet: MR4105547
Digital Object Identifier: 10.1216/jca.2020.12.263

Subjects:
Primary: 13F35, 43A15, 46M40

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 2 • Summer 2020
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