Frobenius and Cartier algebras of Stanley-Reisner rings

2011/06/28 by Josep Álvarez Montaner, Josep Alvarez Montaner, Montaner, Josep Alvarez +4
Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1106.5686

16 pages

arxiv created 2011/06/28 · openalex publication_date 2011/06/28 · arxiv updated 2011/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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