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

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...

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Detalles Bibliográficos
Autor: Thuong, L.Q.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/666
Acceso en línea:http://hdl.handle.net/20.500.11824/666
Access Level:acceso abierto
Palabra clave:Definable sets
Formal schemes
Integral identity conjecture
Motivic integration
Resolution of singularity
Rigid varieties
Volume Poincaré series
Descripción
Sumario: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.