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7 votes
3 answers
915 views

Bounded cohomology motivation

May I ask what is the basic motivation behind studying bounded cohomology? Is there a simple reason why bounded cohomology is more interesting / useful than usual cohomology? Also, is bounded ...
12 votes
6 answers
3k views

applications of Tate-Poitou duality

What are nice applications of Tate-Poitou duality?
6 votes
0 answers
1k views

Relative cohomology in algebraic topology vs algebraic geometry

There is a notion of relative cohomology in both algebraic topology and algebraic geometry and the flexibility granted by this relative viewpoint is quite powerful in both cases. However, the two ...