A generalized-fractions approach to computing local cohomology.

Abstract: This talk aims to describe a method to compute Lyubeznik Numbers in prime characteristic by applying generalized fractions tools to $F$-finite $F$-modules. The main part of the talk will consist of a very brief introduction to local cohomology, Lyubeznik's notion of $F$-finite $F$-modules, and the Sharp-Zakeri theory of generalized fractions. This introduction will be aimed at non-experts.

The final part of the talk will introduce Lyubeznik numbers and show how these can be computed using the tools introduced earlier in the talk. All results are based on a joint project with Rodney Sharp whose results are available in "Lyubeznik numbers, $F$-modules and modules of generalized fractions" (arXiv:2006.05438)

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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