Moduli of unipotent representations I: Foundational topics

With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let G be such a group. The stack M _n(G) of all representations of dimension n is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack M _n ^nd(G) which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by M _n ^nd(G). We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.