engleski

Categories of sheaves and generalizations

Generalizations and analogues of topological spaces, for example noncommutative spaces, spaces with structures, algebraic spaces, bad quotients, may be alternatively described by an analogue of a category of sheaves on a topological space. For example, Serre's theorem on proj of a graded ring and Gabriel-Rosenberg theorem on reconstruction of schemes show this philosophy. We outline a landscape of such theories from derived algebraic geometry to noncommutative algebraic geometry, where the geometric and topological considerations are done from the perspective of (generalized) sheaf theory.

sheaf; quasicoherent sheaf; Grothendieck topology; topos; localization

nije evidentirano