Home /  COMA Colloquium: "Local cohomology, free resolutions, and Tor modules"

Seminar

COMA Colloquium: "Local cohomology, free resolutions, and Tor modules" April 02, 2024 (11:00 AM PDT - 12:00 PM PDT)
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Location: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Marc Chardin (Institut de Mathématiques de Jussieu)
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Local cohomology, free resolutions, and Tor modules

Abstract/Media

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When S is a standard Z-graded polynomial extension of a ring R, the Castelnuovo-Mumford regularity of a graded S-module can be defined in four ways: in terms of vanishing degrees for local cohomology supported in the variables, vanishing degrees for Tor modules, shifts appearing in graded free S-resolutions, and degrees for which the truncation of the module has a linear free resolution. We will present some extensions of the equivalence of these definitions to the more general situation that corresponds to a product of projective spaces over R, in place of a projective space over R. Illustrating examples will concern Rees algebras and points in a product of two projective spaces over a field.

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Local cohomology, free resolutions, and Tor modules