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OP-8620Status unassessedGeometry and topology

Local cohomology in characteristic p

Macaulay2: expanded functionality and improved efficiency · Historical workshop question

Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/macaulay2efie/ Not an author-supplied MSC code.

Historical list · status unassessedAs of 2026-09-08Source & evidence ↓

Problem statement

Given an F-finite F-module, how can one efficiently compute a unit F-module? For example, given the map Exti(R/I,R)→Exti(R/I[p],R)\mathrm{Ext}^i(R/I,R)\to \mathrm{Ext}^i(R/I^{[p]},R), how can one find a root for the local cohomology module HIi(R)H^i_I(R)?

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Background

Question context

If R is a regular ring of characteristic p, then the local cohomology modules have many nice finiteness properties; one can describe many of these properties via the theory of unit FF-modules. Work on implementing these calculations in M2 was begun at the 2023 Minneapolis workshop.

Progress & source assessment

Historical workshop record. Current open/solved status has not been independently reassessed.

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References
  1. [1]Macaulay2: expanded functionality and improved efficiency link

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