1. What is Gersten's conjecture?
1.1 Historical Note
1.2 The case of general dimension
1.3 The case of that A is a commutative discrete valuation ring
1.4 The case for Grothendieck groups
1.5 The case for singular varieties
1.6 Other cohomology theories
1.7 Logical connections with other conjectures
1.8 Counterexample for non-commutative discrete valuation rings (Due to Kazuya Kato)

2. Idea of the proof
2.1 Ring theoretic side
2.2 Homotopy theoretic side

3. Strategy of the proof

4. Split epimorphism theorem

5. Zero map theorem
5.1 Structure of C
5.2 Modified algebraic K-theory
5.3 Homotopy natural transformations

6. Motivic Gersten's conjecture
6.1 Motivic zero map theorem
6.2 Nilpotent invariant motives