Proofs of the integral identity conjecture over algebraically closed fields

TitleProofs of the integral identity conjecture over algebraically closed fields
Publication TypeJournal Article
Year of Publication2015
AuthorsLê, QThuong
JournalDuke Mathematical Journal
Volume164
Start Page157
Issue1
Pagination157-194
Date Published01/2015
Type of ArticleResearch
Keywordsrigid varieties
Abstract

Recently, it has become well known that the conjectural integral identity is of crucial importance in the motivic Donaldson–Thomas invariants theory for noncommutative Calabi–Yau threefolds. The purpose of this article is to consider different versions of the identity, for regular functions and formal functions, and to give them the positive answer for the algebraically closed ground fields. Technically, the result on the motivic Milnor fiber by Hrushovski–Loeser using Hrushovski–Kazhdan’s motivic integration and Nicaise’s computations on motivic integrals on special formal schemes are main tools.

URLhttp://projecteuclid.org/euclid.dmj/1420813016
DOI10.1215/00127094-2869138