About Me

I am a postdoc in the working group of Alexander Schmidt at the Institute for Mathematics at the Faculty of Mathematics and Computer Science at the University of Heidelberg. Furthermore, I am a member of CRC326 - GAUS: "Geometry and Arithmetic of Uniformizing Structures".

During the academic year 2019/20 I was a postdoc in the working group of Andrew Kresch at the Institute of Mathematics at the University of Zurich and financed by the Swiss National Science Foundation. Until September 2019 I was a PhD student at the Faculty of Mathematics at the University of Regensburg. My PhD thesis is about continuous K-theory and its relation to the cohomology of rigid spaces. My advisors were Moritz Kerz and Georg Tamme. I was a member of the DFG GRK 1692 “Curvature, Cycles, and Cohomology” and I was partially supported by the DFG SFB 1085 “Higher Invariants”.

I wrote my master's thesis “Milnor K-theory of integers of p-adic local fields” and my bachelor's thesis “Serres Problem und der Satz von Quillen-Suslin” (Serre's problem and the Quillen-Suslin theorem) both with Moritz Kerz.

Research

My research areas are K-theory and Motivic Homotopy Theory with a focus on rigid analytic spaces.

Publications and Preprints

Motivic homotopy theory for perfect schemes (joint with Jeroen Hekking and Storm Wolters). (arXiv:2510.01390)
Duality for KGL-modules in motivic homotopy theory (joint with Jeroen Hekking and Storm Wolters). (arXiv:2508.00064)
Towards A^1-homotopy theory of rigid analytic spaces (joint with Can Yaylali). (arXiv:2407.09606)
Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory, Comptes Rendus. Mathématique, Volume 363 (2025), pp. 989-1001. (link to journal) (arXiv:2403.02413)
Continuous K-Theory and Cohomology of Rigid Spaces, Manuscripta Mathematica vol. 173 (2024), pp. 119–153. (link to journal) (arXiv:1910.10437)
K-Theory of admissible Zariski-Riemann spaces, Annals of K-Theory vol. 8 (2023), no. 1, pp. 1–23. (link to journal) (arXiv:2101.04131)
On continuous K-theory and cohomology of rigid spaces, PhD thesis, Universität Regensburg (2019). (link)
Milnor K-theory of complete discrete valuation rings with finite residue fields, J. Pure Appl. Algebra vol. 222 (2018), no. 6, pp. 1355–1371. (link to journal) (arXiv:1509.01087)

Notes

A counterexample to pro-cdh descent for non-noetherian schemes (PDF)

Organized Events

09/2023: Fall School "Algebraic K-Theory and Redshift" (together with Lorenzo Mantovani and Georg Tamme)
02/2023: GAUS-workshop "Condensed Mathematics and K-Theory" (together with Georg Tamme)

Talks & Posters

05/2025: Invited talk on Duality in (perfect) motivic homotopy theory at the University of Mainz.
05/2025: Invited talk on Duality in (perfect) motivic homotopy theory at the Seminar on Arithmetic Geometry at Technical University Darmstadt.
05/2024: Invited talk on Towards A^1-homotopy theory of rigid analytic spaces at the Mathematics Institute of the University of Warwick.
11/2023: Invited talk (online) on Representability of analytic K-theory within a rigid analytic motivic homotopy category at the Harish Chandra Research Institute.
11/2023: Invited talk on Representability of analytic K-theory within a rigid analytic motivic homotopy category at the University of Zurich.
12/2020: Invited talk (online) on K-theory of admissible Zariski-Riemann spaces at the University Freiburg.
06/2020: Invited talk on Continuous K-theory and K-theory of Zariski-Riemann spaces at the online conference Motives and What Not.
01/2020: Invited talk on Continuous K-theory and K-theory of Zariski-Riemann spaces at the University of Duisburg-Essen.
05/2019: Invited talk on Continuous K-theory and cohomology of rigid spaces at the University of Heidelberg.
05/2019: Invited talk on Continuous K-theory and cohomology of rigid spaces at the University Freiburg.
07/2018: Poster for the conference Berkovich spaces 30 years in Paris (pdf).
06/2018: Poster for the conference Homotopy Theory Summer in Berlin (pdf).
02/2018: Talk on Continuous K-theory and cohomology of analytic spaces at the conference K-theory, A1-homotopy and quadratic forms in Warwick.
05/2017-06/2017: Participant at the Hausdorff Trimester Program on K-theory and Related Fields in Bonn.
05/2017: Talk on Improved Milnor K-theory of valuation rings of local fields in Bonn (video).

Teaching

University of Heidelberg

WS 2025/26: Seminar Quadratische Formen (Quadratic forms) (together with Alexander Schmidt).
WS 2025/26: Exercise class for the course Étale Cohomology 1 by Alberto Merici.
SS 2025: Seminar p-adische Zahlen (p-adic numbers).
SS 2025: Exercise sheets and example class for the course Algebra 2 by Denis Vogel.
WS 2024/25: Seminar on Quadradische Formen und Milnor-Witt-K-Theorie (Quadratic forms and Milnor-Witt K-theory) (together with Morten Lüders).
SS 2024: Exercise class for the course Étale Kohomologie 2 (Étale Cohomology 2) by Alexander Schmidt.
WS 2023/24: Course Gruppenschemata (Group Schemes).
WS 2023/24: Seminar Homotopical Category Theory (together with Lukas Waas).
SS 2023: Exercise sheets for the course Algebraische Geometrie 2 (Algebraic Geometry 2) by Denis Vogel.
WS 2022/23: Seminar on K-theory of the integers and the Kummer-Vandiver Conjecture (together with Alexander Schmidt).
WS 2022/23: Exercise sheets and example class for the course Algebraische Geometrie 1 (Algebraic Geometry 1) by Denis Vogel.
SS 2022: Exercise sheets for the course Algebraische Zahlentheorie 2 (Algebraic Number Theory 2) by Katharina Hübner.
SS 2022: Exercise sheets for the course Algebra 2 by Denis Vogel.
WS 2021/22: Seminar Bewertungstheorie (Valuation Theory) (together with Katharina Hübner).
SS 2021: Exercise sheets and example class for the course Algebra 2 by Alexander Schmidt.
WS 2020/21: Exercise sheets and example class for the course Algebraische Zahlentheorie 2 (Algebraic Number Theory 2) by Denis Vogel.
WS 2020/21: Seminar p-adische Zahlen (p-adic numbers) (together with Marius Leonhardt).

University of Zurich

FS 2020: Course on Algebra and Topology (together with Lorenzo Mantovani).
HS 2019/20: Seminar on Categories, Sheaves, and Locales.
HS 2019/20: Seminar on Prismatic Cohomology (together with Lorenzo Mantovani).

University of Regensburg

SS 2019: Assistance and exercise class for the course Perfectoid Spaces by Georg Tamme.
SS 2019: Higher Invariants Oberseminar on Resolution of Singularities in characteristic zero (together with Federico Binda and Johann Haas).
WS 2018-19: Seminar on Homotopical Methods (together with Denis-Charles Cisinski).
SS 2018: Seminar on Derived Categories and Sheaf Cohomology (together with Denis-Charles Cisinski).
WS 2014/15: Exercise class for the course Algebra by Patrick Forré.
SS 2014: Exercise class for the course Kommutative Algebra by Uwe Jannsen.
WS 2013/14: Exercise class for the course Algebra by Guido Kings.
WS 2012/13: Exercise class for the course Lineare Algebra I by Guido Kings.
SS 2012: Exercise corrector for the course Einführung in die moderne Logik (Introduction to modern logic) by Tim Kraft.
WS 2011/12: Exercise class for the course Lineare Algebra II by Uwe Jannsen.
SS 2011: Exercise class for the course Lineare Algebra I by Uwe Jannsen.

Curriculum Vitae

Since 10/2020: Postdoc at Heidelberg University.
10/2019-09/2020: Postdoc at University of Zurich.
07/2019: PhD (Dr. rer. nat) in Mathematics at University of Regensburg.
03/2015: Master of Science in Mathematics at University of Regensburg.
03/2013: Bachelor of Science in Mathematics at University of Regensburg.
06/2009: Final secondary exam at Staatliches Landschulheim Marquartstein.

Christian Dahlhausen