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Fernando Sancho

Publications and source records attributed to Fernando Sancho.

5 recordsLinked to original sources
arXiv2021

Relative perfect complexes

Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as a consequence, that a quasi-proper morphism takes relative perfect complexes into perfect ones. We obtain a generalized version of the semicontinuity theorem of dimension of cohomology and Grauert's base change of the fibers. Finally, a bivariant theory of the Grothendieck group of perfect complexes is developed.

math.AG↗
arXiv2021

Notes on schematic finite spaces

The schematic finite spaces are those finite ringed spaces where a theory of quasi-coherent modules can be developed with minimal natural conditions. We give various characterizations of these spaces and their natural morphisms. We show that schematic finite spaces are strongly related to quasi-compact quasi-separated schemes.

math.AG↗
arXiv2017

Geometric characterization of flat modules

Let $R$ be a commutative ring. Roughly speaking, we prove that an $R$-module $M$ is flat iff it is a direct limit of $R$-module affine algebraic varieties, and $M$ is a flat Mittag-Leffler module iff it is the union of its $R$-submodule affine algebraic varieties.

math.AG↗
arXiv2017

Flat SML modules and reflexive functors

We give some functorial characterizations of flat strict Mittag-Leffler modules. We characterize reflexive functors of modules with similar tools, definitions and theorems.

math.AC↗