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Presented By: Student Commutative Algebra Seminar - Department of Mathematics

Student Commutative Algebra: Valuation rings in characteristic p and Abhyankar valuations

Swayam Chube

This is basically an exposition of the paper "Frobenius and Valuation Rings" by Rankeya Datta and Karen Smith. We shall look at the interaction of non-Noetherian valuation rings (i.e., non-DVRs) in char p with the Frobenius endomorphism and give an example of a non-excellent DVR arising as a valuation ring in a function field. We shall also look at a necessary and sufficient condition for a valuation to be Abhyankar.

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