# K-theory of admissible Zariski-Riemann spaces

@inproceedings{Dahlhausen2021KtheoryOA, title={K-theory of admissible Zariski-Riemann spaces}, author={Christian Dahlhausen}, year={2021} }

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 example of a non-noetherian abelian category whose negative K-theory vanishes.

## References

SHOWING 1-10 OF 23 REFERENCES

Algebraic K-theory and descent for blow-ups

- Mathematics
- 2018

We prove that algebraic K-theory satisfies ‘pro-descent’ for abstract blow-up squares of noetherian schemes. As an application we derive Weibel’s conjecture on the vanishing of negative K-groups.

Relative Riemann-Zariski spaces

- Mathematics
- 2008

In this paper we study relative Riemann-Zariski spaces associated to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ…

ON NEGATIVE ALGEBRAIC K-GROUPS

- MathematicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019

We sketch a proof of Weibel’s conjecture on the vanishing of negative algebraic K-groups and we explain an analog of this result for continuous K-theory of nonarchimedean algebras. 1 Negative…

Higher Algebraic K-Theory of Schemes and of Derived Categories

- Mathematics
- 1990

In this paper we prove a localization theorem for the K-theory of commutative rings and of schemes, Theorem 7.4, relating the K-groups of a scheme, of an open subscheme, and of the category of those…

Negative K-theory of derived categories

- Mathematics
- 2006

We define negative K-groups for exact categories and for ``derived categories'' in the framework of Frobenius pairs, generalizing definitions of Bass, Karoubi, Carter, Pedersen-Weibel and Thomason.…

The compactness of the Riemann manifold of an abstract field of algebraic functions

- Mathematics
- 1944

1. The existence of finite resolving systems. In an earlier paper we have announced the result that the existence of a resolving system of the Riemann manifold of an abstract field of algebraic…

Algebraic Geometry

- MathematicsNature
- 1973

Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)

Milnor excision for motivic spectra

- MathematicsJournal für die reine und angewandte Mathematik
- 2021

Abstract We prove that the ∞{\infty}-category of motivic spectra satisfies Milnor excision: if A→B{A\to B} is a morphism of commutative rings sending an ideal I⊂A{I\subset A} isomorphically onto an…