Deligne–Riemann–Roch and intersection bundles

Dennis Eriksson; Gerard Freixas i Montplet

doi:10.5802/jep.254

Deligne–Riemann–Roch and intersection bundles
[Deligne-Riemann-Roch et fibrés d’intersection]

Dennis Eriksson ¹ ; Gerard Freixas i Montplet ²

¹ Department of Mathematics, Chalmers University of Technology and University of Gothenburg, 412 96 Göteborg, Sweden
² C.N.R.S., Centre de Mathématiques Laurent Schwartz, École Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau cedex, France

Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 247-361.

Résumé
Abstract

Cet article fait partie d’une série de travaux des auteurs ayant pour objectif de compléter un vaste programme énoncé par Deligne, visant à relever la partie de codimension $1$ du théorème de Grothendieck-Riemann-Roch des classes d’isomorphisme de fibrés en droites à des isomorphismes canoniques. L’article développe une théorie d’intersection fonctorielle relative à valeurs dans les fibrés en droites, avec un formalisme qui généralise les constructions précédentes de Deligne et Elkik, liées au côté droit du théorème.

This article is part of a series of works by the authors with the goal of completing a far-reaching program propounded by Deligne, aiming to extend the codimension one part of the Grothendieck–Riemann–Roch theorem from isomorphism classes of line bundles to canonical isomorphisms thereof. The paper develops a relative functorial intersection theory with values in line bundles, together with a formalism that generalizes previous constructions by Deligne and Elkik, related to the right-hand side of the theorem.

Reçu le : 2023-06-08
Accepté le : 2024-01-12
Publié le : 2024-01-26

DOI : 10.5802/jep.254

Classification : 14C17, 19D99, 14C40, 19D23
Keywords: Deligne program, virtual categories, intersection bundles, Grothendieck–Riemann–Roch, categorification
Mot clés : Programme de Deligne, catégories virtuelles, fibrés d’intersection, Grothendieck-Riemann-Roch, catégorification

Affiliations des auteurs :

Dennis Eriksson ¹ ; Gerard Freixas i Montplet ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Dennis Eriksson; Gerard Freixas i Montplet. Deligne–Riemann–Roch and intersection bundles. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 247-361. doi : 10.5802/jep.254. https://jep.centre-mersenne.org/articles/10.5802/jep.254/

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