Topos theory in algebraic geometry

Nathan Lowry, September 15, 2023

Through Grothendieck's functor-of-points perspective, categorical structures can often be studied through an internal language. A category needs appropriate additional structure for such a logic; in particular, an elementary topos has an intuitionistic higher-order internal language. In this talk, we will examine the internal logic of a category of sheaves associated to a scheme and use it to prove a nontrivial result in algebraic geometry.