Proofs of the integral identity conjecture over algebraically closed fields

Abstract

Recently, it is well known that the conjectural integral identity is of crucial importance in the motivic Donaldson-Thomas invariants theory for non-commutative 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 ground field algebraically closed. Technically, the result on 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.

arXiv commentto appear in Duke Mathematical Journal

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• Motivic Igusa zeta functions
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Cited by in corpus (12)

• Purity for graded potentials and quantum cluster positivity
• The motivic Donaldson-Thomas invariants of (-2) curves
• Monodromy and the Lefschetz fixed point formula
• Motivic DT-invariants for the one loop quiver with potential
• A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory
• A proof of the integral identity conjecture, II
• The motivic Thom-Sebastiani theorem for regular and formal functions
• HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
• Deformed dimensional reduction
• Donaldson-Thomas invariants of length 2 flops
• Equivariant motivic integration and proof of the integral identity conjecture for regular functions
• Bounded integral and motivic Milnor fiber