UC San Diego

Formal schemes are (topologically) ringed spaces that Grothendieck introduced in EGA. They are simultaneously analogues for admissible rings of schemes for general commutative rings and a “bridge” between analytic and algebraic geometry. More recently, formal schemes have been a subject of interest in studies of rigid analytic geometry, where, due to work by Raynaud, Bosch, and Lütkebohmert, they act as models for rigid analytic varieties. The recent interest in these objects has led to study of them in their own right. In this thesis, we investigate whether a minimal model program could exist for formal schemes.