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Yuichiro Taguchi

2009-05-20
13:40:00 - 14:30:00

Extensions of truncated discrete valuation rings

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

A truncated discrete valuation ring is a commutative ring which is isomorphic to a quotient of finite length of a discrete valuation ring. We give an equivalence between the category of at most a-ramified finite separable extensions of a complete discrete valuation field K and the category of at most a-ramified finite extensions of the \length-a truncation" of the integer ring of K. This extends a theorem of Deligne, in which he proved this fact assuming the residue field is perfect. Our theory depends heavily on Abbes-Saito's ramification theory. This is a joint work with Toshiro Hiranouchi.