Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Finiteness conditions for local cohomology modules

Seminar | November 5 | 3:45-4:45 p.m. | 939 Evans Hall

 Robin Hartshorne, UC Berkeley

 Department of Mathematics

The local cohomology modules of a module M over a commutative noetherian ring A with supports in an ideal I are rarely finitely generated. I will describe two recent theories, that of D-modules in char. 0, and F-modules in char. p >0, where the additional structure allows one to factor a module into a composition series with simple quotients. This has applications, for example, in studying the cohomology of a variety in projective space. I expect to spend more time on the char. p case, which seems to be less well-known.