Hodge-Tate stacks and non-abelian p-adic Hodge theory of v-perfect complexes on rigid spaces

Let X be a quasi-compact quasi-separated p-adic formal scheme that is smooth either over a perfectoid Z p-algebra or over some ring of integers of a p-adic field. We construct a fully faithful functor from perfect complexes on the Hodge-Tate stack of X up to isogeny to perfect complexes on the v-site of the generic fibre of X. Moreover, we describe perfect complexes on the Hodge-Tate stack in terms of certain derived categories of Higgs and Higgs-Sen modules. This leads to a derived p-adic Simpson functor.