7 papers
Representability of continuous K-theory in rigid analytic motivic -homotopy theory
Christian Dahlhausen, Can Yaylali, Yicheng Zhou
We prove that both continuous K-theory and analytic K-theory of rigid analytic spaces (à la Kerz--Saito--Tamme) satisfiy descent with respect to the Nisnevich topology. Together wi…
Motivic homotopy theory for perfect schemes
Christian Dahlhausen, Jeroen Hekking, Storm Wolters
We construct a perfect version of Morel--Voevodsky's motivic homotopy category over a perfect base scheme in positive characteristic. By checking the axioms of a coefficient system…
Duality for KGL-modules in motivic homotopy theory
Christian Dahlhausen, Jeroen Hekking, Storm Wolters
We prove a duality statement on modules over KH-theory in the stable motivic homotopy category whose dualizing object is given by G-theory, over any quasi-excellent scheme of chara…
Towards -homotopy theory of rigid analytic spaces
Christian Dahlhausen, Can Yaylali
To any rigid analytic space (in the sense of Fujiwara--Kato) we assign an -invariant rigid analytic homotopy category with coefficients in any presentable category. W…
Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory
Christian Dahlhausen
We show that the algebraic K-theory of semi-valuation rings with stably coherent regular semi-fraction ring satisfies homotopy invariance. Moreover, we show that these rings are re…
K-theory of admissible Zariski-Riemann spaces
Christian Dahlhausen
We study relative algebraic K-theory of admissible Zariski-Riemann spaces and prove that it is equivalent to G-theory and satisfies homotopy invariance. Moreover, we provide an exa…