Commutative Algebra seminar
Thursday, 5 Oct. 3.30-5.00 pm
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Venue: Ramanujan Hall
Host: Tony Puthenpurakal
Speaker: Jugal Verma, IIT Bombay
Title: Local cohomology and Hilbert functions-1
Abstract: In this series of four lectures, I will prove the Grothendieck-Serre (GS) formula for the difference between the Hilbert function and the Hilbert polynomial of a graded module over a standard graded ring. I will also prove some of its variations for the Hilbert-Samuel polynomial using the local cohomology of Rees algebras. The first lecture will review the basic results of local cohomology modules needed for the later lectures. An important invariant of the Hilbert function is its postulation number. We will see that the Castelnuovo-Mumford regularity is an upper bound on the postulation number. In the later lectures, we shall show how the GS -formula yields unified proofs of many results due to Sally, Rossi-Valla, and Huneke-Ooishi, about Hilbert-Samuel polynomial of m-primary ideals in local rings.