62 The Trace Formula

Section 62.1: Introduction
Section 62.2: The trace formula
- Equation 62.2.0.1
Section 62.3: Frobenii
- Exercise 62.3.1
- Lemma 62.3.2
- Theorem 62.3.3: The Baffling Theorem
- Definition 62.3.4
- Lemma 62.3.5
- Remark 62.3.6
- Lemma 62.3.7
- Definition 62.3.8
- Theorem 62.3.9
- Definition 62.3.10
  - Equation 62.3.10.1
- Remark 62.3.11
Section 62.4: Traces
- Definition 62.4.1
- Exercise 62.4.2
Section 62.5: Why derived categories?
Section 62.6: Derived categories
- Remark 62.6.1
- Lemma 62.6.2
- Lemma 62.6.3
- Definition 62.6.4
- Remark 62.6.5
Section 62.7: Filtered derived category
- Definition 62.7.1
- Lemma 62.7.2
Section 62.8: Filtered derived functors
- Definition 62.8.1
- Proposition 62.8.2
Section 62.9: Application of filtered complexes
Section 62.10: Perfectness
- Definition 62.10.1
- Proposition 62.10.2
Section 62.11: Filtrations and perfect complexes
- Lemma 62.11.1: Additivity
- Lemma 62.11.2
Section 62.12: Characterizing perfect objects
- Definition 62.12.1
- Lemma 62.12.2
- Remark 62.12.3
Section 62.13: Cohomology of nice complexes
- Proposition 62.13.1
Section 62.14: Lefschetz numbers
- Definition 62.14.1
- Definition 62.14.2
- Theorem 62.14.3: Lefschetz Trace Formula
  - Equation 62.14.3.1
- Theorem 62.14.4: Weil
- Example 62.14.5
- Lemma 62.14.6
Section 62.15: Preliminaries and sorites
- Lemma 62.15.1
- Definition 62.15.2
- Lemma 62.15.3
- Lemma 62.15.4
- Lemma 62.15.5
- Lemma 62.15.6
- Lemma 62.15.7
- Lemma 62.15.8
- Lemma 62.15.9
- Remark 62.15.10
Section 62.16: Proof of the trace formula
- Theorem 62.16.1
  - Equation 62.16.1.1
- Remark 62.16.2
- Remark 62.16.3
Section 62.17: Applications
Section 62.18: On l-adic sheaves
- Definition 62.18.1
- Lemma 62.18.2
- Lemma 62.18.3
- Example 62.18.4
- Remark 62.18.5
- Definition 62.18.6
- Remark 62.18.7
- Definition 62.18.8
Section 62.19: L-functions
- Definition 62.19.1
- Remark 62.19.2
- Definition 62.19.3
Section 62.20: Cohomological interpretation
- Theorem 62.20.1: Finite Coefficients
- Theorem 62.20.2: Adic sheaves
- Remark 62.20.3
- Theorem 62.20.4
- Theorem 62.20.5
- Lemma 62.20.6
Section 62.21: List of things which we should add above
Section 62.22: Examples of L-functions
Section 62.23: Constant sheaves
- Lemma 62.23.1
- Exercise 62.23.2
Section 62.24: The Legendre family
Section 62.25: Exponential sums
Section 62.26: Trace formula in terms of fundamental groups
Section 62.27: Fundamental groups
- Definition 62.27.1
- Theorem 62.27.2: Grothendieck
- Proposition 62.27.3
- Theorem 62.27.4: Deligne, Weil II
Section 62.28: Profinite groups, cohomology and homology
Section 62.29: Cohomology of curves, revisited
- Lemma 62.29.1
- Remark 62.29.2
- Proposition 62.29.3
- Remark 62.29.4
Section 62.30: Abstract trace formula
- Remark 62.30.1
- Example 62.30.2
Section 62.31: Automorphic forms and sheaves
- Definition 62.31.1
- Theorem 62.31.2
- Theorem 62.31.3
- Remark 62.31.4
- Proposition 62.31.5
- Lemma 62.31.6
- Lemma 62.31.7
- Theorem 62.31.8
- Theorem 62.31.9
- Theorem 62.31.10
Section 62.32: Counting points
Section 62.33: Precise form of Chebotarev
Section 62.34: How many primes decompose completely?
- Proposition 62.34.1
Section 62.35: How many points are there really?