Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/193802
Title: | Frobenius and Cartier algebras of Stanley-Reisner rings |
Author: | Àlvarez Montaner, Josep Fernandez Boix, Alberto Zarzuela, Santiago |
Keywords: | Geometria algebraica Anells commutatius Anells associatius Topologia algebraica Algebraic geometry Commutative rings Associative rings Algebraic topology |
Issue Date: | 15-May-2012 |
Publisher: | Elsevier |
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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.jalgebra.2012.03.006 |
It is part of: | Journal of Algebra, 2012, vol. 358, p. 162-177 |
URI: | http://hdl.handle.net/2445/193802 |
Related resource: | https://doi.org/10.1016/j.jalgebra.2012.03.006 |
ISSN: | 0021-8693 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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