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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Morphisms between two constructions of Witt vectors of non-commutative rings
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by Supriya Pisolkar PDF
Proc. Amer. Math. Soc. 148 (2020), 2835-2842 Request permission

Abstract:

Let $A$ be any unital associative, possibly non-commutative ring and let $p$ be a prime number. Let $E(A)$ be the ring of $p$-typical Witt vectors as constructed by Cuntz and Deninger in [J. Algebra 440 (2015), pp. 545–593] and let $W(A)$ be the abelian group constructed by Hesselholt in [Acta Math. 178 (1997), pp. 109–141] and [Acta Math. 195 (2005), pp. 55–60]. In [J. Algebra 506 (2018), pp. 379–396] it was proved that if $p=2$ and $A$ is a non-commutative unital torsion free ring, then there is no surjective continuous group homomorphism from $W(A) \to HH_0(E(A)): = E(A)/\overline {[E(A),E(A)]}$ which commutes with the Verschiebung operator and the Teichmüller map. In this paper we generalise this result to all primes $p$ and simplify the arguments used for $p=2$. We also prove that if $A$ a is a non-commutative unital ring, then there is no continuous map of sets $HH_0(E(A)) \to W(A)$ which commutes with the ghost maps.
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Additional Information
  • Supriya Pisolkar
  • Affiliation: Indian Institute of Science, Education and Research (IISER), Homi Bhabha Road, Pashan, Pune - 411008, India
  • MR Author ID: 868359
  • Email: supriya@iiserpune.ac.in
  • Received by editor(s): April 28, 2019
  • Received by editor(s) in revised form: November 13, 2019
  • Published electronically: March 30, 2020
  • Additional Notes: This work was supported by the SERB-MATRICS grant MTR/2018/000346.
  • Communicated by: Sarah Witherspoon
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 2835-2842
  • MSC (2010): Primary 16S99; Secondary 13F35
  • DOI: https://doi.org/10.1090/proc/14992
  • MathSciNet review: 4099773