Deligne-Riemann-Roch Theorems I. Uniqueness of Deligne Pairings and Degree 1 Part of Deligne-Riemann-Roch Isomorphisms

2017/10/26 by Mingchen Xia, Xia, Mingchen
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1710.09731

openalex publication_date 2017/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the first of a series of papers. Our final goal is to establish Deligne-Riemann-Roch isomorphisms in various settings. In this paper, we establish a uniqueness theorem for Deligne pairings and prove the degree 1 part of the Deligne-Riemann-Roch theorem.

Citations

• An arithmetic Riemann-Roch theorem

Related

• On Deligne's functorial Riemann-Roch theorem in positive characteristic
• The Deligne pairing and a functorial Riemann Roch theorem in positive characteristic
• The Deligne-Riemann-Roch isomorphism
• Riemann-Roch for Deligne-Mumford stacks
• Deligne-Riemann-Roch and intersection bundles