Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism u:R⟶U. Assuming that the ring epimorphism is homological of flat/projective dimension 1, we discuss the abelian categories of u-comodules and u-contramodules and construct the recollement of unbounded derived categories of R-modules, U-modules, and complexes of R-modules with u-co/contramodule cohomology. Further assumptions allow to describe the third category in the recollement as the unbounded derived category of the abelian categories of u-comodules and u-contramodules. For commutative rings, we also prove that any homological epimorphism of projective dimension 1 is flat. Injectivity of the map u is not required.

Matlis category equivalences for a ring epimorphism

Bazzoni S.
;
2020

Abstract

Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism u:R⟶U. Assuming that the ring epimorphism is homological of flat/projective dimension 1, we discuss the abelian categories of u-comodules and u-contramodules and construct the recollement of unbounded derived categories of R-modules, U-modules, and complexes of R-modules with u-co/contramodule cohomology. Further assumptions allow to describe the third category in the recollement as the unbounded derived category of the abelian categories of u-comodules and u-contramodules. For commutative rings, we also prove that any homological epimorphism of projective dimension 1 is flat. Injectivity of the map u is not required.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3337720
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