We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes.
In an earlier paper the notion of a filtered derived equivalence was introduced, and it was shown that if two K3 surfaces admit such an equivalence then they are isomorphic. In this paper we study more refined aspects of filtered derived equivalences related to the action on the cohomological realizations of the Mukai motive. It is shown that if a filtered… (More)
~ 1 ~ " As our case is new, so we must think anew and act anew " Abraham Lincoln Abstract This report covers an intelligent decision support system (IDSS), which handles an efficient and effective way to rapidly inspect containerized cargos for defection. Defection is either cargo exposure to radiation, physical damages such as holes, punctured surfaces,… (More)
Geometric invariant theory and derived categories of coherent sheaves Abstract Geometric invariant theory and derived categories of coherent sheaves Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its geometric invariant theory quotient.… (More)