60 The Trace Formula

Section 60.1: Introduction
Section 60.2: The trace formula
- Equation 60.2.0.1
Section 60.3: Frobenii
- Exercise 60.3.1
- Lemma 60.3.2
- Theorem 60.3.3: The Baffling Theorem
- Definition 60.3.4
- Lemma 60.3.5
- Remark 60.3.6
- Lemma 60.3.7
- Definition 60.3.8
- Theorem 60.3.9
- Definition 60.3.10
  - Equation 60.3.10.1
- Remark 60.3.11
Section 60.4: Traces
- Definition 60.4.1
- Exercise 60.4.2
Section 60.5: Why derived categories?
Section 60.6: Derived categories
- Remark 60.6.1
- Lemma 60.6.2
- Lemma 60.6.3
- Definition 60.6.4
- Remark 60.6.5
Section 60.7: Filtered derived category
- Definition 60.7.1
- Lemma 60.7.2
Section 60.8: Filtered derived functors
- Definition 60.8.1
- Proposition 60.8.2
Section 60.9: Application of filtered complexes
Section 60.10: Perfectness
- Definition 60.10.1
- Proposition 60.10.2
Section 60.11: Filtrations and perfect complexes
- Lemma 60.11.1: Additivity
- Lemma 60.11.2
Section 60.12: Characterizing perfect objects
- Definition 60.12.1
- Lemma 60.12.2
- Remark 60.12.3
Section 60.13: Cohomology of nice complexes
- Proposition 60.13.1
Section 60.14: Lefschetz numbers
- Definition 60.14.1
- Definition 60.14.2
- Theorem 60.14.3: Lefschetz Trace Formula
  - Equation 60.14.3.1
- Theorem 60.14.4: Weil
- Example 60.14.5
- Lemma 60.14.6
Section 60.15: Preliminaries and sorites
- Lemma 60.15.1
- Definition 60.15.2
- Lemma 60.15.3
- Lemma 60.15.4
- Lemma 60.15.5
- Lemma 60.15.6
- Lemma 60.15.7
- Lemma 60.15.8
- Lemma 60.15.9
- Remark 60.15.10
Section 60.16: Proof of the trace formula
- Theorem 60.16.1
  - Equation 60.16.1.1
- Remark 60.16.2
- Remark 60.16.3
Section 60.17: Applications
Section 60.18: On l-adic sheaves
- Definition 60.18.1
- Lemma 60.18.2
- Lemma 60.18.3
- Example 60.18.4
- Remark 60.18.5
- Definition 60.18.6
- Remark 60.18.7
- Definition 60.18.8
Section 60.19: L-functions
- Definition 60.19.1
- Remark 60.19.2
- Definition 60.19.3
Section 60.20: Cohomological interpretation
- Theorem 60.20.1: Finite Coefficients
- Theorem 60.20.2: Adic sheaves
- Remark 60.20.3
- Theorem 60.20.4
- Theorem 60.20.5
- Lemma 60.20.6
Section 60.21: List of things which we should add above
Section 60.22: Examples of L-functions
Section 60.23: Constant sheaves
- Lemma 60.23.1
- Exercise 60.23.2
Section 60.24: The Legendre family
Section 60.25: Exponential sums
Section 60.26: Trace formula in terms of fundamental groups
Section 60.27: Fundamental groups
- Definition 60.27.1
- Theorem 60.27.2: Grothendieck
- Proposition 60.27.3
- Theorem 60.27.4: Deligne, Weil II
Section 60.28: Profinite groups, cohomology and homology
Section 60.29: Cohomology of curves, revisited
- Lemma 60.29.1
- Remark 60.29.2
- Proposition 60.29.3
- Remark 60.29.4
Section 60.30: Abstract trace formula
- Remark 60.30.1
- Example 60.30.2
Section 60.31: Automorphic forms and sheaves
- Definition 60.31.1
- Theorem 60.31.2
- Theorem 60.31.3
- Remark 60.31.4
- Proposition 60.31.5
- Lemma 60.31.6
- Lemma 60.31.7
- Theorem 60.31.8
- Theorem 60.31.9
- Theorem 60.31.10
Section 60.32: Counting points
Section 60.33: Precise form of Chebotarev
Section 60.34: How many primes decompose completely?
- Proposition 60.34.1
Section 60.35: How many points are there really?