Tate-Betti and Tate-Bass numbers
Edgar Enochs, Sergio Estrada, Alina Iacob
TL;DR
This paper introduces Tate-Betti and Tate-Bass invariants for modules over local rings, proves their periodicity over hypersurfaces, and establishes their equality for modules and their Matlis duals in Gorenstein rings.
Contribution
It defines new invariants for modules over local rings and proves their periodicity and duality properties, extending understanding of module invariants in algebraic geometry.
Findings
Tate-Betti and Tate-Bass invariants are well-defined for modules over local rings.
These invariants are periodic when the ring is a hypersurface.
Modules and their Matlis duals share the same invariants in Gorenstein rings.
Abstract
We define Tate-Betti and Tate-Bass invariants for modules over a commutative noetherian local ring R. Then we show the periodicity of these invariants provided that R is a hypersurface. In case R is also Gorenstein, we show that a finitely generated R-module M and its Matlis dual have the same Tate-Betti and Tate-Bass numbers.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Advanced Topics in Algebra