[Une preuve de la version -adique de la conjecture de l’identité intégrale pour des polynômes]
It is well known that the integral identity conjecture is of prime importance in Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for non-commutative Calabi-Yau threefolds. In this article we consider its numerical version and give a complete demonstration of the case where the potential is a polynomial and the ground field is algebraically closed. The fundamental tool is the Berkovich spaces whose crucial point is how to use the comparison theorem for nearby cycles as well as the Künneth isomorphism for cohomology with compact support.
Il est bien connu que la conjecture de l’identité intégrale est de première importance de la théorie de Kontsevich-Soibelman des invariants de Donaldson-Thomas motiviques pour des variétés de Calabi-Yau de dimension 3 non commutatives. Dans cet article nous considérons sa version numérique et donnons une complète démonstration dans le cas où le potentiel est un polynôme et le corps de base est algébriquement clos. L’outil fondamental pour la preuve est les espaces de Berkovich dont le point crucial est l’utilisation du théorème de comparaison entre des cycles proches ainsi que l’isomorphisme de Künneth en cohomologie à support compact.
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DOI : 10.24033/bsmf.2785
Keywords: Berkovich spaces, étale cohomology for Berkovich spaces, formal scheme, formal nearby cycles functor, generic fiber, motivic Milnor fiber
Mots-clés : Espaces de Berkovich, la cohomologie étale des espaces de Berkovich, schéma formel, des cycles proches formels, fibre générique, fibre de Milnor motivique
Thuong, Lê Quy 1
@article{BSMF_2019__147_3_355_0,
author = {Thuong, L\^e Quy},
title = {A proof of the $\ell $-adic version of the integral identity conjecture for polynomials},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {355--375},
year = {2019},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {147},
number = {3},
doi = {10.24033/bsmf.2785},
mrnumber = {4030543},
zbl = {1441.14070},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2785/}
}
TY - JOUR AU - Thuong, Lê Quy TI - A proof of the $\ell $-adic version of the integral identity conjecture for polynomials JO - Bulletin de la Société Mathématique de France PY - 2019 SP - 355 EP - 375 VL - 147 IS - 3 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2785/ DO - 10.24033/bsmf.2785 LA - en ID - BSMF_2019__147_3_355_0 ER -
%0 Journal Article %A Thuong, Lê Quy %T A proof of the $\ell $-adic version of the integral identity conjecture for polynomials %J Bulletin de la Société Mathématique de France %D 2019 %P 355-375 %V 147 %N 3 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2785/ %R 10.24033/bsmf.2785 %G en %F BSMF_2019__147_3_355_0
Thuong, Lê Quy. A proof of the $\ell $-adic version of the integral identity conjecture for polynomials. Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 3, pp. 355-375. doi: 10.24033/bsmf.2785
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