Integral Grothendieck–Riemann–Roch theorem

2007/03/11 by G. Pappas · 13 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Factorization #Gravitational singularity #Grothendieck group #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Pure mathematics #Resolution (logic) #Resolution of singularities #Riemann hypothesis #Torsion (gastropod) #math.AG

paper · pdf · doi:10.1007/s00222-007-0067-9

published in Inventiones mathematicae 170(3), 455-481 (Springer Science+Business Media) · 24 pages

arxiv created 2007/03/11 · openalex publication_date 2007/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.

Citations

• Théorie des Intersections et Théorème de Riemann-Roch
• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I
• Le théorème de Riemann-Roch
• Topological Methods in Algebraic Geometry