Spahn duality

The term duality can refer to many notions. Most of them are instances of the notion of dual category?. Often a duality is formulated in terms of cohomology?.

• dual category?

• dual vector space?

• Poincaré duality? for finite dimensional (oriented) closed manifolds

• Pontryagin duality? for commutative (Hausdorff?) topological groups?

• Cartier duality of a finite flat commutative group scheme?

• Serre duality? on nonsingular projective algebraic varieties which has as a special case the statement of the Rieman-Roch theorem?

• Grothendieck duality?, coherent duality? for coherent sheaves?

• Verdier duality? for abelian categories of sheaves; e.g. for a category of sheaves of abelian groups.

• Artin-Verdier duality? generalizing Tate duality? for constructible sheaves over the spectrum of a ring of algebraic numbers?.