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A Short Survey on the Integral Identity Conjecture and Theories of Motivic Integration

Authors
  • Thuong, Lê Quy1, 2
  • 1 Vietnam National University, Department of Mathematics, 334 Nguyen Trai Street, Thanh Xuan District, Hanoi, Vietnam , Thanh Xuan District (Vietnam)
  • 2 BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, Basque Country, E-48009, Spain , Bilbao (Spain)
Type
Published Article
Journal
Acta Mathematica Vietnamica
Publisher
Springer Singapore
Publication Date
Dec 19, 2016
Volume
42
Issue
2
Pages
289–310
Identifiers
DOI: 10.1007/s40306-016-0197-5
Source
Springer Nature
Keywords
License
Yellow

Abstract

In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these invariants. A purpose of this note is to show how the conjecture arises. Because of the integral identity’s nature, we shall give a quick tour on theories of motivic integration, which lead to a proof of the conjecture for algebraically closed ground fields of characteristic zero.

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