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.

to appear in Duke Mathematical Journal

References in corpus (6)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Desingularization of quasi-excellent schemes in characteristic zero
• A trace formula for rigid varieties, and motivic Weil generating series for formal schemes
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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