ℓ-adic cohomology and trace formulas
Eleven lessons on adic cohomology and trace methods, with complete arguments, worked examples, exercises and solutions.
- ℓ-adic sheaves and their cohomology
- The pro-étale site and ℓ-adic complexes
- Frobenius morphisms and their action on cohomology
- Traces of perfect complexes and Lefschetz numbers
- Cycle classes and the Lefschetz fixed-point formula for curves
- The trace formula for curves
- The trace formula in all dimensions
- L-functions, rationality and the functional equation
- Lefschetz pencils and vanishing cycles
- The fundamental estimate
- The Riemann hypothesis over finite fields
Supporting readings and prerequisites · Sources and terms · Download the reader and editable sources
All eleven lessons are included. Each reading identifies its mathematical prerequisites and supporting proofs.