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J. R. Garcia-Rozas

Publications and source records attributed to J. R. Garcia-Rozas.

3 recordsLinked to original sources
arXiv2007

Gorenstein categories and Tate cohomology on projective schemes

We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov-Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a category has what Hovey calls an injective model structure and also a projective model structure in case the category has enough projectives. As examples we show that if X is a locally Gorenstein projective scheme then the category Qco(X) of quasi-coherent sheaves on $X$ is such a category and so has these features.

math.CT↗
arXiv2007

Locally projective monoidal model structure for complexes of quasi-coherent sheaves on P^1(k)

We will generalize the projective model structure in the category of unbounded complexes of modules over a commutative ring to the category of unbounded complexes of quasi-coherent sheaves over the projective line. Concretely we will define a locally projective model structure in the category of complexes of quasi-coherent sheaves on the projective line. In this model structure the cofibrant objects are the dg-locally projective complexes. We also describe the fibrations of this model structure and show that the model structure is monoidal. We point out that this model structure is necessarily different from other known model structures such as the injective model structure and the locally free model structure.

math.AG↗