Algebraic $\mathbb{A}^{1}$-invariance of K-theory for affinoid Tate adic spaces of good reduction

Abstract

We establish homotopy invariance for connective continuous K-theory of affinoid Tate adic spaces of good reduction with respect to the algebraic affine line, distinct from the adic affine line as analytic stacks. We approach this through an investigation of boundedness of t-structures on nuclear module categories, to which end we also study ultrasolid modules, a variant of solid modules, and their properties.