| Abstract |
Local cohomology was introduced by Grothendieck in the early sixties, in part to answer a conjecture of Pierre Samuel about when certain types of commutative rings are unique factorization domains. 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 about projective varieties that were originally proved in other ways.
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