63 The Trace Formula
-
Section 63.1: Introduction
-
Section 63.2: The trace formula
-
Section 63.3: Frobenii
-
Section 63.4: Traces
-
Section 63.5: Why derived categories?
-
Section 63.6: Derived categories
-
Section 63.7: Filtered derived category
-
Section 63.8: Filtered derived functors
-
Section 63.9: Application of filtered complexes
-
Section 63.10: Perfectness
-
Section 63.11: Filtrations and perfect complexes
-
Section 63.12: Characterizing perfect objects
-
Section 63.13: Cohomology of nice complexes
-
Section 63.14: Lefschetz numbers
-
Section 63.15: Preliminaries and sorites
-
Section 63.16: Proof of the trace formula
-
Section 63.17: Applications
-
Section 63.18: On l-adic sheaves
-
Section 63.19: L-functions
-
Section 63.20: Cohomological interpretation
-
Section 63.21: List of things which we should add above
-
Section 63.22: Examples of L-functions
-
Section 63.23: Constant sheaves
-
Section 63.24: The Legendre family
-
Section 63.25: Exponential sums
-
Section 63.26: Trace formula in terms of fundamental groups
-
Section 63.27: Fundamental groups
-
Section 63.28: Profinite groups, cohomology and homology
-
Section 63.29: Cohomology of curves, revisited
-
Section 63.30: Abstract trace formula
-
Section 63.31: Automorphic forms and sheaves
-
Section 63.32: Counting points
-
Section 63.33: Precise form of Chebotarev
-
Section 63.34: How many primes decompose completely?
-
Section 63.35: How many points are there really?