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Frobenius and Cartier algebras of Stanley-Reisner rings

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Álvarez Montaner, JosepMés informacióMés informacióMés informació
Boix, Alberto F.
Zarzuela Armengou, Santiago
Document typeResearch report
Defense date2011-09
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
We study the generation of the Frobenius algebra of the injective hull of a complete Stanley-Reisner ring over a field with positive characteristic. In particular, by extending the ideas used by M. Katzman to give a counterexample to a question raised by G. Lyubeznik and K. E. Smith about the finite generation of Frobenius algebras, we prove that the Frobenius algebra of the injective hull of a complete Stanley-Reisner ring can be only principally generated or infinitely generated. Also, by using our explicit description of the generators of such algebra and applying the recent work by M. Blickle about Cartier algebras and generalized test ideals, 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 subset inside the non-negative real numbers
Is part of[prepr201106AlvBZ]
URIhttp://hdl.handle.net/2117/13372
URL other repositoryhttp://www.ma1.upc.edu/recerca/preprints2011.html
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  • EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions - Reports de recerca [103]
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