Let f: X -> Y be a projective (or locally Moishezon and proper) surjective morphism of integral quasi-excellent Noetherian schemes (or algebraic spaces/formal schemes) or of integral analytic spaces (complex or non-Archimedean in the sense of Tate, Berkovich, or Huber). In this talk, I will present my GAGA theorems (joint with Shiji Lyu) for Grothendieck duality and two applications.

First, in equal characteristic zero, I will show vanishing and injectivity theorems for f as above using our GAGA theorems and the analogous results I proved for schemes. As far as I am aware, these are the first vanishing theorems proved for non-projective morphisms of non-Archimedean analytic spaces in arbitrary dimension. These methods recover theorems of Nakayama for locally Moishezon morphisms of complex analytic spaces.

Second, in arbitrary characteristic, I will explain how our GAGA theorems imply new results for the relative minimal model program with scaling for f either when Y is of equal characteristic zero or when dim(X) ≤ 3.