Nonarchimedean factorization theorems via factorization algebras

We formulate an analogue of factorization algebras theory over a nonarchimedean field K, building on work of Costello and Gwilliam in the complex analytic case. Several constructions involved in factorization algebras theory, leading to a wealth of standard examples, are developed in the nonarchimedean setting. En route, we build aspects of Jacob Lurie's Verdier duality theory in the rigid analytic setting. Last, an analogue of the factorization theorems traditionally studied in rational conformal field theory, as in Faltings' work on the Verlinde Formula, is developed in the nonarchimedean setting by interpreting nodal degenerations of smooth algebraic curves in terms of nonarchimedean gluing.