Thu, October 4, 2018
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2:00pm [2:00pm] J. K. Verma
Description:
Commutative algebra seminar Thursday, 4 October, 2018 Room 215 2.00-3.30 Speaker: J. K. Verma Title: The Hoskin-Deligne formula for complete ideals in two-dimensional regular local rings. Abstract: Let I be a complete m-primary ideal in a two dimensional regular local ring R. The Hoskin-Deligne (HD) formula expresses the length of the Artin local ring R/I in terms of the m-adic order of the transforms of I in various local quadratic transforms of R. It uses a structure theorem of Zariski and Abhyankar about two dimensional regular local rings which birationally dominate R. The HD formula implies several fundamental theorems about complete ideals proved by Zariski, Lipman, Rees and Huneke-Sally. We shall prove these in a series of talks.

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