We define a category of smooth 1-motives with torsion over a locally noetherian base scheme and prove its Cartier duality. More precisely, we prove that …
We study Serre functors and related constructions. A Serre functor on a triangulated category was defined by Bondal and Kapranov to be an auto-equivalence inducing …
In this thesis, we consider rank one perturbations A_a=A+a(.,f)f of a self-adjoint operator A with cyclic vector f in H_{-1}(A) on a Hilbert space H. …