On basic and Bass quaternion orders
Authors:
Sara Chari, Daniel Smertnig and John Voight
Journal:
Proc. Amer. Math. Soc. Ser. B 8 (2021), 11-26
DOI:
https://doi.org/10.1090/bproc/68
Published electronically:
January 13, 2021
MathSciNet review:
4199211
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Abstract | References | Additional Information
Abstract: A quaternion order $\mathcal {O}$ over a Dedekind domain $R$ is Bass if every $R$-superorder is Gorenstein, and $\mathcal {O}$ is basic if it contains an integrally closed quadratic $R$-order. In this article, we show that these conditions are equivalent in local and global settings: a quaternion order is Bass if and only if it is basic. In particular, we show that the property of being basic is a local property of a quaternion order.
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Additional Information
Sara Chari
Affiliation:
Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
MR Author ID:
1341376
Email:
schari0301@gmail.com
Daniel Smertnig
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
MR Author ID:
916775
Email:
dsmertni@uwaterloo.ca
John Voight
Affiliation:
Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
MR Author ID:
727424
ORCID:
0000-0001-7494-8732
Email:
jvoight@gmail.com
Received by editor(s):
March 14, 2019
Received by editor(s) in revised form:
October 31, 2020
Published electronically:
January 13, 2021
Additional Notes:
The second author was supported by the Austrian Science Fund (FWF) project J4079-N32.
The third author was supported by an NSF CAREER Award (DMS-1151047) and a Simons Collaboration Grant (550029).
Communicated by:
Benjamin Brubaker
Article copyright:
© Copyright 2021
by the authors under
Creative Commons Attribution 3.0 License
(CC BY 3.0)
