G-dimension over local homomorphisms. Applications to the Frobenius endomorphism

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We develop a theory of G-dimension for modules over local homomorphisms which encompasses the classical theory of G-dimension for finite modules over local rings. As an application, we prove that a local ring R of characteristic p is Gorenstein if and only if it possesses a nonzero finite module of finite projective dimension that has finite G-dimension when considered as an R-module via some power of the Frobenius endomorphism of R. We also prove results that track the behavior of Gorenstein properties of local homomorphisms under (de)composition.
31 pages, uses Xy-pic

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Commutative Algebra, Algebraic Geometry, 13D05, 13D25, 13B10, 13H10, 14B25

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http://salesiana.dossiersoluciones.com/handle/123456789/66853

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303265
 http://arxiv.org/abs/math/0303265

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arXiv