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Event SMS Weekly Talk
Date 02/23/2017
Time 02:30
Venue SMS Seminar Room
Title Grothendieck’s Local Cohomology
Speaker Azeem Khadam

Local cohomology was introduced by Grothendieck in the early 1960’s, in part to answer a conjecture of Pierre Samuel about when certain types of commutative rings are unique factorization domains. According to Wikipedia, he introduced it in a series of lectures in Harvard, later written up by Hartshorne, see [1]. Local cohomology modules can be used to measure the depth of a module on an ideal, and as a way to test the Cohen-Macaulay properties. Moreover, the cohomology of coherent sheaves on projective varieties can be recovered from graded components of local cohomology modules, providing useful insights into theorems aboutprojective varieties that were originally proved in other ways.

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