A proof of the $\ell$-adic version of the integral identity conjecture for polynomials

Details A proof of the $\ell$-adic version of the integral identity conjecture for polynomials A proof of the $\ell$-adic version of the integral identity conjecture for polynomials

2012-04-08

arxiv.org/abs/1204.1758v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

We consider the $\ell$-adic version of the integral identity conjecture and give a complete proof in the case of polynomials. This conjecture is among of the key foundations of the theory of motivic Donaldson-Thomas invariants for non-commutative 3d Calabi-Yau varieties, which was introduced recently by Kontsevich and Soibelman. Our approach is to use some results on the Berkovich spaces, specially the comparison theorem for nearby cycles and the K$\ddot{\text{u}}$nneth isomorphism for cohomology with compact support.

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