Algebraický seminář
Paolo Stellari (Univ. Milano): From Fourier-Mukai kernels to internal Homs and back
Abstract: One key problem in the theory of triangulated categories of geometric nature (e.g. bounded derived categories of coherent sheaves on sufficiently nice schemes) is about an efficient description of exact functors. The work of Mukai, Orlov and others seemed to suggest that this could be addressed by means of the theory of Fourier-Mukai functors. More recently, the seminal work of To\"en and a new higher categorical viewpoint suggested that one should approach this issue by investigating their higher categorical liftability by interpreting them as objects in appropriate internal Homs categories. We explain in which sense these two perspectives coincide by generalizing a result by Lunts-Schnürer and thus giving a complete proof of an unproven claim by Toën. This requires the proof of a claim of Kontsevich and Keller about internal Homs and recent results about uniqueness of dg enhancements. This is a joint work (partly in progress) with Alberto Canonaco and Mattia Ornaghi.
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.
