Representability of cohomological functors over extension fields

  • Alice Rizzardo

    SISSA, Trieste, Italy

Abstract

We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor to the case where is a field extension of the base field of the variety , with trdeg or purely transcendental of degree 2.

This result can be applied to investigate the behavior of an exact functor with and smooth projective varieties and dim or a rational surface. We show that for any such there exists a "generic kernel" in , such that is isomorphic to the Fourier–Mukai transform with kernel after composing both with the pullback to the generic point of .

Cite this article

Alice Rizzardo, Representability of cohomological functors over extension fields. J. Noncommut. Geom. 11 (2017), no. 4, pp. 1267–1287

DOI 10.4171/JNCG/11-4-2