This paper surveys the recent advances concerning the relations between triangulated (or
derived) categories and their dg enhancements. We explain when some interesting …

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 …

Twisted Hodge diamonds give rise to non-Fourier–Mukai functors Page 1 J. Noncommut.
Geom. 18 (2024), 891–952 DOI 10.4171/JNCG/543 © 2023 European Mathematical Society …

A celebrated result by Orlov states that any fully faithful exact functor between the bounded
derived categories of coherent sheaves on smooth projective varieties is of geometric origin …

In this thesis, we study a class of derived equivalences that naturally induce birational maps.
We give several equivalent criteria for a birational correspondence to exist, and prove the …

Nella mia tesi di Dottorato mi sono occupato della relazione tra la più importante classe di
funtori tra categorie derivate, ovvero quella dei funtori di Fourier-Mukai, ei quasi-funtori che …

1.1. Общий обзор курса. Мы будем изучать производные категории когерентных пучков
на алгебраических многообразиях. Я предполагаю, что слушатели уже знают, что …

Classical homological algebra can roughly be thought of as the study of functors taking
geometric objects (eg manifolds) to simple algebraic invariants (eg abelian groups). Around …

Motivated by the Chern-Weil theory, we prove that for a given vector bundle $ E $ on a
smooth scheme $ X $ over a field $ k $ of any characteristic, the Chern classes of $ E $ in …