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july 2020 $G$-valuations and $G$-valuation rings
Nikolaas D. Verhulst
Bull. Belg. Math. Soc. Simon Stevin 27(2): 281-298 (july 2020). DOI: 10.36045/bbms/1594346418

Abstract

We aim to construct a non-commutative algebraic geometry in the style of Chevalley by using generalised valuations. To this end, we introduce groupoid valuation rings and associate suitable value functions to them. We show that many results from classical valuation theory can be generalised in a natural way to this context and give several examples. In the final section, we give a very concrete example of what a non-commutative curve would look like in this new setting.

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Nikolaas D. Verhulst. "$G$-valuations and $G$-valuation rings." Bull. Belg. Math. Soc. Simon Stevin 27 (2) 281 - 298, july 2020. https://doi.org/10.36045/bbms/1594346418

Information

Published: july 2020
First available in Project Euclid: 10 July 2020

zbMATH: 07242769
MathSciNet: MR4121374
Digital Object Identifier: 10.36045/bbms/1594346418

Subjects:
Primary: 16W50, 16W60

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 2 • july 2020
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