Algebraic Geometry Seminar

The derived category of coherent sheaves of a variety is an object that is relevant to the study of moduli spaces, birational geometry, mirror symmetry, and more. Many results characterizing when the derived categories of two complex surfaces are equivalent are known, including a theorem of Sosna that the canonical cover of an Enriques surface is not derived equivalent to any varieties other than itself, and that the canonical cover of a bielliptic surface is derived equivalent to at most one other variety. In this talk I will discuss methods used to prove this result over algebraically closed fields of positive characteristic at least 5.