Moduli spaces in rigid geometry -- Evan Warner, October 6, 2017
Until recently, the only technique to prove representability results in rigid geometry went via the theory of formal models. This suffices to construct, e.g., the Quot/Hilb spaces in sufficient generality, but not the Picard space pararmetrizing invertible line bundles on a proper rigid variety. By proving and using a version of Artin's representability criteria in the rigid setting in addition to the formal methods, I will construct this Picard space under certain hypotheses. Key to this development is the thoroughgoing use of the theory of adic spaces.