Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Twisted derived categories and Rouquier functors

Martin Olsson

Abstract

We study the algebraic structure of the automorphism group of the derived category of coherent sheaves on a smooth projective variety twisted by a Brauer class. Our main results generalize results of Rouquier in the untwisted case.

Twisted derived categories and Rouquier functors

Abstract

We study the algebraic structure of the automorphism group of the derived category of coherent sheaves on a smooth projective variety twisted by a Brauer class. Our main results generalize results of Rouquier in the untwisted case.
Paper Structure (17 sections, 21 theorems, 64 equations)

This paper contains 17 sections, 21 theorems, 64 equations.

Table of Contents

  1. Statements of results
  2. Acknowledgements
  3. Twisted sheaves
  4. Proof of Theorem \ref{['T:theorem1']} (1) and (2)
  5. Proof of \ref{['T:theorem1']} (1)
  6. Proof of \ref{['T:theorem1']} (2)
  7. Proof of Theorem \ref{['T:theorem1']} (3)
  8. Proof of theorem \ref{['T:theorem2']}
  9. Proof of \ref{['T:theorem2']}
  10. The action of $\mathcal{R} _{\mathcal{X} }$ on $D(\mathcal{X} )$
  11. The action on $D(X, \alpha )$.
  12. Proof of theorem \ref{['T:theorem3']}
  13. Compatibility with convolution.
  14. Completion of proof of \ref{['T:theorem3']}
  15. Twisted derived category of abelian variety
  16. ...and 2 more sections

Key Result

Theorem 1.1

(1) The fibered category $\mathcal{A}ut _{\mathcal{X} }$ is an algebraic stack locally of finite type over $k$ which is a $\mathbf{G}_m$-gerbe over a group algebraic space $\text{\rm Aut} _{\mathcal{X} }$. (2) If $\text{\rm Aut} ^0_{\mathcal{X} }\subset \text{\rm Aut} _{\mathcal{X} }$ denotes the co (3) If $\mathcal{X}$ is the pushout of a $\mu _N$-gerbe for $N>0$ invertible in $k$ (this always ho

Theorems & Definitions (52)

  • Theorem 1.1
  • Example 1.2
  • Definition 1.3
  • Remark 1.4
  • Example 1.5
  • Theorem 1.7
  • Remark 1.8
  • Theorem 1.9
  • Remark 1.10
  • Lemma 2.1
  • ...and 42 more