7 citations · 15 across the 7 of their papers we have counts for
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New examples of non-Fourier-Mukai functors
Theo Raedschelders, Alice Rizzardo, Michel Van den Bergh
In this paper we prove that any smooth projective variety of dimension equipped with a tilting bundle can serve as the source variety of a non-Fourier-Mukai functor between…
A k-linear triangulated category without a model
Alice Rizzardo, Michel Van den Bergh
In this paper we give an example of a triangulated category, linear over a field of characteristic zero, which does not carry a DG-enhancement. The only previous examples of triang…
A note on non-unique enhancements
Alice Rizzardo, Michel Van den Bergh
We give an easy example of a triangulated category, linear over a field , with two different enhancements, linear over , answering a question of Canonaco and Stellari.
Adjoints to a Fourier-Mukai transform
Alice Rizzardo
Given a Fourier-Mukai functor in the general setting of singular schemes, under various hypotheses we provide both left and a right adjoints to , and also give explicit form…
An example of a non-Fourier-Mukai functor between derived categories of coherent sheaves
Alice Rizzardo, Michel Van den Bergh, Amnon Neeman
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…
Representability of cohomological functors over extension fields
Alice Rizzardo
We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor from the bounded derived category of a smooth projective variety over a field t…
Scalar extensions of derived categories and non-Fourier-Mukai functors
Alice Rizzardo, Michel Van den Bergh
Orlov's famous representability theorem asserts that any fully faithful functor between the derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai…
On the existence of Fourier-Mukai kernels
Alice Rizzardo
A theorem by Orlov states that any equivalence between the bounded derived categories of coherent sheaves of two smooth projective varieties, X and Y, is isomorphic to a Fourier-Mu…