64 The Trace Formula

Section 64.1: Introduction
Section 64.2: The trace formula
- Equation 64.2.0.1
Section 64.3: Frobenii
- Exercise 64.3.1
- Lemma 64.3.2
- Theorem 64.3.3: The Baffling Theorem
- Definition 64.3.4
- Lemma 64.3.5
- Remark 64.3.6
- Lemma 64.3.7
- Definition 64.3.8
- Theorem 64.3.9
- Definition 64.3.10
  - Equation 64.3.10.1
- Remark 64.3.11
Section 64.4: Traces
- Definition 64.4.1
- Exercise 64.4.2
Section 64.5: Why derived categories?
Section 64.6: Derived categories
- Remark 64.6.1
- Lemma 64.6.2
- Lemma 64.6.3
- Definition 64.6.4
- Remark 64.6.5
Section 64.7: Filtered derived category
- Definition 64.7.1
- Lemma 64.7.2
Section 64.8: Filtered derived functors
- Definition 64.8.1
- Proposition 64.8.2
Section 64.9: Application of filtered complexes
Section 64.10: Perfectness
- Definition 64.10.1
- Proposition 64.10.2
Section 64.11: Filtrations and perfect complexes
- Lemma 64.11.1: Additivity
- Lemma 64.11.2
Section 64.12: Characterizing perfect objects
- Definition 64.12.1
- Lemma 64.12.2
- Remark 64.12.3
Section 64.13: Cohomology of nice complexes
- Proposition 64.13.1
Section 64.14: Lefschetz numbers
- Definition 64.14.1
- Definition 64.14.2
- Theorem 64.14.3: Lefschetz Trace Formula
  - Equation 64.14.3.1
- Theorem 64.14.4: Weil
- Example 64.14.5
- Lemma 64.14.6
Section 64.15: Preliminaries and sorites
- Lemma 64.15.1
- Definition 64.15.2
- Lemma 64.15.3
- Lemma 64.15.4
- Lemma 64.15.5
- Lemma 64.15.6
- Lemma 64.15.7
- Lemma 64.15.8
- Lemma 64.15.9
- Remark 64.15.10
Section 64.16: Proof of the trace formula
- Theorem 64.16.1
  - Equation 64.16.1.1
- Remark 64.16.2
- Remark 64.16.3
Section 64.17: Applications
Section 64.18: On l-adic sheaves
- Definition 64.18.1
- Lemma 64.18.2
- Lemma 64.18.3
- Example 64.18.4
- Remark 64.18.5
- Definition 64.18.6
- Remark 64.18.7
- Definition 64.18.8
Section 64.19: L-functions
- Definition 64.19.1
- Remark 64.19.2
- Definition 64.19.3
Section 64.20: Cohomological interpretation
- Theorem 64.20.1: Finite Coefficients
- Theorem 64.20.2: Adic sheaves
- Remark 64.20.3
- Theorem 64.20.4
- Theorem 64.20.5
- Lemma 64.20.6
Section 64.21: List of things which we should add above
Section 64.22: Examples of L-functions
Section 64.23: Constant sheaves
- Lemma 64.23.1
- Exercise 64.23.2
Section 64.24: The Legendre family
Section 64.25: Exponential sums
Section 64.26: Trace formula in terms of fundamental groups
Section 64.27: Fundamental groups
- Definition 64.27.1
- Theorem 64.27.2: Grothendieck
- Proposition 64.27.3
- Theorem 64.27.4: Deligne, Weil II
Section 64.28: Profinite groups, cohomology and homology
Section 64.29: Cohomology of curves, revisited
- Lemma 64.29.1
- Remark 64.29.2
- Proposition 64.29.3
- Remark 64.29.4
Section 64.30: Abstract trace formula
- Remark 64.30.1
- Example 64.30.2
Section 64.31: Automorphic forms and sheaves
- Definition 64.31.1
- Theorem 64.31.2
- Theorem 64.31.3
- Remark 64.31.4
- Proposition 64.31.5
- Lemma 64.31.6
- Lemma 64.31.7
- Theorem 64.31.8
- Theorem 64.31.9
- Theorem 64.31.10
Section 64.32: Counting points
Section 64.33: Precise form of Chebotarev
Section 64.34: How many primes decompose completely?
- Proposition 64.34.1
Section 64.35: How many points are there really?