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An example of a non-Fourier-Mukai functor between derived categories of coherent sheaves

Alice Rizzardo

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Abstract

Orlov's famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. In this paper we show that this result is false without the full faithfulness hypothesis.

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What this paper is about

Orlov's famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. In this paper we show that this result is false without the full faithfulness hypothesis.

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Available abstract

Orlov's famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. In this paper we show that this result is false without the full faithfulness hypothesis.

Key concepts: Functor, Mathematics, Pure mathematics, Coherent sheaf, Exact functor, Bounded function, Derived category, Algebra over a field

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