The Deligne-Riemann-Roch isomorphism
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909939423772672 |
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| author | Eriksson, Dennis Montplet, Gerard Freixas i |
| author_facet | Eriksson, Dennis Montplet, Gerard Freixas i |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Deligne-Riemann-Roch isomorphism Eriksson, Dennis Montplet, Gerard Freixas i Algebraic Geometry 14C40, 19D23, 14C17, 19D99 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. |
| title | The Deligne-Riemann-Roch isomorphism |
| topic | Algebraic Geometry 14C40, 19D23, 14C17, 19D99 |
| url | https://arxiv.org/abs/2509.05077 |