RÉSUMÉ

In this talk I will present results obtained by joint-work with Gunther Cornelissen (Gent Univ./Max-Planck-Institut in Bonn) on deformations of ordinary/Mumford curves together with automorphisms in positive characteristics. This research was motivated from our past research, by Aristeides Kondogeorgis (Univ. of Crete) and us, on bounding the order of automorphism groups of Mumford curves. The talk will focus to, as well as the main results, some examples, arised from that past work, in which interesting phenomena can be seen both algebraically and analytically. The talk will start by observing two motivating examples, including that of Drinfeld modular curves, of such a deformation, which will be elucidated by the results on algebraic and analytic deformation theory at the end of the talk.

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