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Derived invariants and motives, Part I, Integral Grothendieck Riemann-Roch and non-commutative motives

2022/06/10 by Keiho Matsumoto, Matsumoto, Keiho
Mathematics · #14C15 #14F08 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2206.04825

openalex publication_date 2022/06/10 · openalex created_date 2022/06/14 · openalex updated_date 2026/07/28

Abstract

The goal of this series of papers is to give a new non-commutative approach to problems about the density of reductions such as the conjecture of Joshi-Rajan, and the generalization of the conjecture of Serre. In this paper, we prove integral Grothendieck Riemann-Roch which was proved by Papas in the case ch(k)=0. As a corollary we prove an integral analogue of Kontsevich's comparison theorem, and we show that if a smooth projective variety X has a full exceptional collection then there is an explicit formula of the motive of X up to bounded torsion.

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