We introduce a variant of homotopy -theory for Tate rings, which we call analytic -theory. It is homotopy invariant with respect to the analytic affine line viewed as an ind-object of closed disks of increasing radii. Under a certain regularity assumption we prove an analytic analog of the Bass fundamental theorem and we compare analytic -theory with continuous -theory, which is defined in terms of models. Along the way we also prove some results about the algebraic -theory of Tate rings.
Cite this article
Moritz Kerz, Shuji Saito, Georg Tamme, -Theory of Non-Archimedean Rings. I. Doc. Math. 24 (2019), pp. 1365–1411DOI 10.4171/DM/707