The ACVF theory and motivic Milnor fibers
Speaker: Le Quy Thuong (Vietnam National University)

Time: 15h15, Friday, July 16, 2021

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Meeting ID: 827 7229 2046

Passcode: 830392

Abstract: In this talk, I review recent studies on the theory of algebraically closed value fields of equal charactersistic zero (ACVF theory) developed by Hrushovski-Kazhdan and Hrushovski-Loeser. More precisely, I consider a concrete Grothendieck ring of definable subsets in the VF-sort and prove the structure theorem of this ring which can be presented via materials from extended residue field sort and value group sort. One can construct a ring homomorphism HL from this ring to the Grothendieck ring of algebraic varieties, from which the motivic Milnor fiber can be described in terms of a certain definable subset in VF-sort. As applications, I sketch proofs of the integral identity conjecture and the motivic Thom-Sebastiani theorem using HL, as well as mention the recent work of Fichou-Yin in the same topic.

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