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Proceedings of the American Mathematical Society Series B

Published by the American Mathematical Society since 2014, this gold open access, electronic-only journal is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 2330-1511

The 2020 MCQ for Proceedings of the American Mathematical Society Series B is 0.95.

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Coherence of absolute integral closures
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by Shravan Patankar HTML | PDF
Proc. Amer. Math. Soc. Ser. B 9 (2022), 75-89

Abstract:

We prove that the absolute integral closure $R^{+}$ of an equicharacteristic zero noetherian complete local domain $R$ is not coherent, provided $\dim (R)\geq 2$. As a corollary, we give an elementary proof of the mixed characteristic version of the result due to Asgharzadeh and extend it to dimension $3$.
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Additional Information
  • Shravan Patankar
  • Affiliation: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045
  • Email: spatan5@uic.edu
  • Received by editor(s): September 15, 2021
  • Received by editor(s) in revised form: November 4, 2021, and December 20, 2021
  • Published electronically: March 29, 2022
  • Communicated by: Claudia Polini
  • © Copyright 2022 by the author under Creative Commons Attribution-NonCommercial 3.0 License (CC BY NC 3.0)
  • Journal: Proc. Amer. Math. Soc. Ser. B 9 (2022), 75-89
  • MSC (2020): Primary 13D22, 13A35, 13B22, 13G99
  • DOI: https://doi.org/10.1090/bproc/121
  • MathSciNet review: 4402048