Frobenius and Cartier algebras of Stanley-Reisner rings
Josep Alvarez Montaner, Alberto F. Boix, Santiago Zarzuela
TL;DR
This paper investigates the structure of Frobenius and Cartier algebras in Stanley-Reisner rings, revealing conditions for their generation and implications for the discreteness of F-jumping numbers.
Contribution
It establishes that these algebras are either principally generated or infinitely generated, and shows the discreteness of F-jumping numbers in this context.
Findings
Frobenius algebra can be principally or infinitely generated
Cartier algebra shares similar generation properties
F-jumping numbers form a discrete set in this setting
Abstract
We prove that the Frobenius algebra of the injective hull of a complete Stanley-Reisner ring as well as its Matlis dual notion of Cartier algebra can be only principally generated or infinitely generated. As a consequence we are able to show that the set of F-jumping numbers of generalized test ideals associated to complete Stanley-Reisner rings form a discrete set.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras