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Acta Mathematica Vietnamica

, Volume 42, Issue 2, pp 289–310 | Cite as

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

  • Lê Quy ThuongEmail author
Article

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.

Keywords

Motivic integration Formal schemes Rigid varieties Volume Poincaré series Resolution of singularity Integral identity conjecture Definable sets 

Mathematics Subject Classification (2010)

Primary 03C60 14B20 14E18 14G22 32S45 11S80 

Notes

Acknowledgments

The author sincerely thanks the Basque Centre for Applied Mathematics (BCAM) for hospitality during his visit.

This research is funded by the Vietnam National University, Hanoi (VNU) under project number QG.16.06. This research is also supported by ERCEA Consolidator Grant 615655 - NMST and by the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of MathematicsVietnam National UniversityThanh Xuan DistrictVietnam
  2. 2.BCAM - Basque Center for Applied MathematicsBilbaoSpain

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