We extend the construction of the normal cone of a closed embedding of schemes to any locally morphism of finite type of higher Artin stacks and show that in the Deligne-Mumford case our construction recovers the relative intrinsic normal cone of Behrend and Fantechi. We characterize our extension as the unique one satisfying a short list of axioms, and use it to construct the deformation to the normal cone. As an application of our methods, we associate to any morphism of Artin stacks equipped with a choice of a global perfect obstruction theory a relative virtual fundamental class in the Chow group of Kresch.
Nous étendons la construction du cône normal d’une immersion fermée de schémas à tout morphisme localement de type fini de champs d’Artin supérieurs et montrons que dans le cas de Deligne-Mumford notre construction retrouve le cône normal intrinsèque relatif de Behrend et Fantechi. Nous caractérisons notre extension comme l’unique satisfaisant une courte liste d’axiomes, et l’utilisons pour construire la déformation du cône normal. Comme application de nos méthodes, nous associons à tout morphisme de champs d’Artin muni d’un choix d’une théorie d’obstruction parfaite globale une classe fondamentale virtuelle relative dans le groupe de Chow de Kresch.
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Keywords: Moduli space, normal cone, deformation theory, Artin stack, Chow group
Mot clés : Espace des modules, cône normal, théorie des déformations, champs d’Artin, groupe de Chow
Aranha, Dhyan 1; Pstrągowski, Piotr 2
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TY - JOUR AU - Aranha, Dhyan AU - Pstrągowski, Piotr TI - The Intrinsic Normal Cone for Artin Stacks JO - Annales de l'Institut Fourier PY - 2024 SP - 71 EP - 120 VL - 74 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3583/ DO - 10.5802/aif.3583 LA - en ID - AIF_2024__74_1_71_0 ER -
%0 Journal Article %A Aranha, Dhyan %A Pstrągowski, Piotr %T The Intrinsic Normal Cone for Artin Stacks %J Annales de l'Institut Fourier %D 2024 %P 71-120 %V 74 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3583/ %R 10.5802/aif.3583 %G en %F AIF_2024__74_1_71_0
Aranha, Dhyan; Pstrągowski, Piotr. The Intrinsic Normal Cone for Artin Stacks. Annales de l'Institut Fourier, Volume 74 (2024) no. 1, pp. 71-120. doi : 10.5802/aif.3583. https://aif.centre-mersenne.org/articles/10.5802/aif.3583/
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