The Deligne-Riemann-Roch isomorphism
Algebraic Geometry
2025-12-03 v2
Abstract
This work establishes the geometric component of Deligne's longstanding program on refined Grothendieck-Riemann-Roch formulas expressed through determinants of cohomology. The approach relies on a newly developed universal category of Chern classes together with an associated relative intersection theory. As an example of the applications, we provide a structural description of the coefficients in the Knudsen-Mumford expansion and establish a fundamental Mumford-type isomorphism for the alternating product of Griffiths bundles.
Keywords
Cite
@article{arxiv.2509.05077,
title = {The Deligne-Riemann-Roch isomorphism},
author = {Dennis Eriksson and Gerard Freixas i Montplet},
journal= {arXiv preprint arXiv:2509.05077},
year = {2025}
}
Comments
Sequel to "DELIGNE-RIEMANN-ROCH AND INTERSECTION BUNDLES", DOI : 10.5802/jep.254. See Arxiv version arXiv:2305.13129 . Minor updates with respect to presentation