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arXiv · 2509.05077

The Deligne-Riemann-Roch isomorphism

Dennis Eriksson·Gerard Freixas i Montplet
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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.

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Dennis Eriksson, Gerard Freixas i Montplet. 2025-09-05. The Deligne-Riemann-Roch isomorphism. https://arxiv.org/abs/2509.05077

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