Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Morphisms between two constructions of Witt vectors of non-commutative rings


Author: Supriya Pisolkar
Journal: Proc. Amer. Math. Soc. 148 (2020), 2835-2842
MSC (2010): Primary 16S99; Secondary 13F35
DOI: https://doi.org/10.1090/proc/14992
Published electronically: March 30, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 16S99, 13F35

Retrieve articles in all journals with MSC (2010): 16S99, 13F35


Additional Information

Supriya Pisolkar
Affiliation: Indian Institute of Science, Education and Research (IISER), Homi Bhabha Road, Pashan, Pune - 411008, India
Email: supriya@iiserpune.ac.in

DOI: https://doi.org/10.1090/proc/14992
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
Article copyright: © Copyright 2020 American Mathematical Society