Frobenius and Cartier algebras of Stanley-Reisner rings
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...
| Autores: | , , |
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| Formato: | informe técnico |
| Fecha de publicación: | 2011 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/13372 |
| Acesso em linha: | https://hdl.handle.net/2117/13372 |
| Access Level: | acceso abierto |
| Palavra-chave: | Frobenius algebras Rings (Algebra) Stanley-Reisner rings Cartier algebras Anells (Àlgebra) Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Resumo: | 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 |
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