Appendix: Introduction to Derived Categories of Coherent Sheaves

  title={Appendix: Introduction to Derived Categories of Coherent Sheaves},
  author={Andreas Hochenegger},
  journal={Lecture Notes of the Unione Matematica Italiana},
  • A. Hochenegger
  • Published 22 January 2019
  • Mathematics
  • Lecture Notes of the Unione Matematica Italiana
In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety. 

Figures from this paper

Explicit Deligne pairing
  • Paolo Dolce
  • Mathematics
    European Journal of Mathematics
  • 2021
We give an explicit formula for the Deligne pairing for proper and flat morphisms $$f:X\rightarrow S$$ f : X → S of schemes, in terms of the determinant of cohomology. The whole
On Ulrich bundles on projective bundles
  • A. Hochenegger
  • Mathematics
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • 2021
In this article, the existence of Ulrich bundles on projective bundles $${{\mathbb {P}}}({{\mathcal {E}}}) \rightarrow X$$ P ( E ) → X is discussed. In the case, that the base variety X is


Equivalences of derived categories and K3 surfaces
We consider derived categories of coherent sheaves on smooth projective variaties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a
Methods of Homological Algebra
Considering homological algebra, this text is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory are
This paper surveys some recent results about Fourier-Mukai functors. In particular, given an exact functor between the bounded derived categories of coherent sheaves on two smooth projective
Fourier-Mukai transforms in algebraic geometry
Preface 1. Triangulated categories 2. Derived categories: a quick tour 3. Derived categories of coherent sheaves 4. Derived category and canonical bundle I 5. Fourier-Mukai transforms 6. Derived
The Additivity of Traces in Triangulated Categories
Abstract We explain a fundamental additivity theorem for Euler characteristics and generalized trace maps in triangulated categories. The proof depends on a refined axiomatization of symmetric
Derived automorphism groups of K3 surfaces of Picard rank $1$
We give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a K3 surface of Picard rank 1. We do this by proving that a distinguished
Fourier-Mukai Transforms in Algebraic Geometry
s of 35 posters from various branches of mathematics. A part of the book is devoted to some problems of the interrelationship of mathematics and human society. The book is valuable not only for
Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces
We survey the basic theory of non-commutative K3 surfaces, with a particular emphasis to the ones arising from cubic fourfolds. We focus on the problem of constructing Bridgeland stability conditions
Derived equivalences of K3 surfaces and orientation
Every Fourier-Mukai equivalence between the derived categories of two K3 surfaces induces a Hodge isometry of their cohomologies viewed as Hodge structures of weight two endowed with the Mukai
Foundations of Grothendieck Duality for Diagrams of Schemes
Joseph Lipman: Notes on Derived Functors and Grothendieck Duality.- Derived and Triangulated Categories.- Derived Functors.- Derived Direct and Inverse Image.- Abstract Grothendieck Duality for