JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 23, Number 4, October 2010, Pages 909–966 S 0894-0347(10)00669-7 Article electronically published on April 1, 2010
INTEGRAL TRANSFORMS AND DRINFELD CENTERS IN DERIVED ALGEBRAIC GEOMETRY
DAVID BEN-ZVI, JOHN FRANCIS, AND DAVID NADLER
Compact objects are as necessary to this subject as air to breathe.
R.W. Thomason to A. Neeman, [N3]
Contents 1. Introduction 910 1.1. Perfect stacks 911 1.2. Tensors and functors 913 1.3. Centers and traces 914 1.4. Hecke categories 916 1.5. Topological field theory 917 2. Preliminaries 919 2.1. ∞-categories 919 2.2. Monoidal ∞-categories 921 2.3. Derived algebraic geometry 923 2.4. Derived loop spaces 925 2.5. En-structures 926 3. Perfect stacks 927 3.1. Definition of perfect stacks 927 3.2. Base change and the projection formula 932 3.3. Constructions of perfect stacks 934 4. Tensor products and integral transforms 939 4.1. Tensor products of ∞-categories 940 4.2. Sheaves on fiber products 944 4.3. General base stacks 948 5. Applications 951 5.1. Centers and traces 951 5.2. Centers of convolution categories 954 5.3. Higher centers 957 6. Epilogue: Topological field theory 960 6.1. Topological field theory from perfect stacks 960 6.2. Deligne-Kontsevich conjectures for derived centers 962
Received by the editors October 23, 2008 and, in revised form, March 4, 2010. 2010 Mathematics Subject Classification. Primary 14-XX; Secondary 55-XX.