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

Keiho Matsumoto

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arXiv · 2206.04825

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

Keiho Matsumoto

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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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Keiho Matsumoto. 2022-06-10. Derived invariants and motives, Part I, Integral Grothendieck Riemann-Roch and non-commutative motives. https://arxiv.org/abs/2206.04825

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