Fourier-Mukai partners of K3 surfaces in positive characteristic

By Max Lieblich, Martin Olsson. 2011

62 citations recorded by the source corpus.

We study Fourier-Mukai equivalence of K3 surfaces in positive characteristic and show that the classical results over the complex numbers all generalize. The key result is a positive-characteristic version of the Torelli theorem that uses the derived category in place of the Hodge structure on singular cohomology; this is proven by algebraizing formal lifts of Fourier-Mukai kernels to characteristic zero. As a consequence, any Shioda-supersingular K3 surface is uniquely determined up to isomorphism by its derived category of coherent sheaves. We also study different realizations of Mukai's Hodge structure in algebraic cohomology theories (etale, crystalline, de Rham) and use these to prove: 1) the zeta function of a K3 surface is a derived invariant (discovered independently by Huybrechts); 2) the variational crystalline Hodge conjecture holds for correspondences arising from Fourier-Mukai kernels on products of two K3 surfaces.

Subfields: Geometry and Topology, Mathematical Physics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/6bf425096820af62813882c9279cef7a36cb9ee8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. D. Huybrechts
2. E. Markman
3. Kieran G. O’Grady
4. P. Stellari
5. Emanuele Macrì
6. Keiji Oguiso
7. Ulrike Riess
8. Justin Sawon

In Mathematical Physics

1. D. Huybrechts
2. P. Stellari
3. Emanuele Macrì
4. E. Markman
5. Keiji Oguiso
6. Ulrike Riess
7. D. Joyce
8. Arend Bayer

In Pharmacology

1. D. Huybrechts

Citations in the corpus

• Lectures on K3 Surfaces (2016, methodology): “For the time being, there is only one paper that deals with this, namely Lieblich and Olsson’s [369], to which we refer for details.”