Derived Hom Spaces in Rigid Analytic Geometry

We construct a derived enhancement of Hom spaces between rigid analytic spaces. It encodes the hidden deformation-theoretic information underlying classical moduli space. The main tool in our construction is representability theorem geometry, which has been established previous work. provides us with sufficient and necessary conditions for an functor to possess structure stack. In order verify theorem, we prove several general results context non-archimedean geometry: Tate acyclicity, projection formula, proper base change. These also merit independent interest. Our motivation comes from enumerative geometry. subsequent works, will apply mapping stacks obtain Gromov–Witten invariants.