• Corpus ID: 211069404

Vanishing of Nil-terms and negative K-theory for additive categories

@article{Bartels2020VanishingON,
  title={Vanishing of Nil-terms and negative K-theory for additive categories},
  author={Arthur Bartels and Wolfgang Lueck},
  journal={arXiv: K-Theory and Homology},
  year={2020}
}
We extend notions such as Noetherian, regular, or regular coherent for rings to additive categories. We show that well-known properties for rings carry over to additive categories. For instance, the negative K-groups and all twisted Nil-groups vanish for an additive category if it is regular. Moreover, the additive category of twisted finite Laurent series associated to any automorphism of a Noetherian or regular additive category is again Noetherian or regular. 

On the K-theory of $\mathbb{Z}$-categories

. We relate the notions of Noetherian, regular coherent and regular n -coherent category for Z -linear categories with finitely many objects with the corresponding notions for unital rings. We use

On the algebraic K-theory of Hecke algebras

Consider a totally disconnected group G, which is covirtually cyclic, i.e., contains a normal compact open subgroup L such that G/L is infinite cyclic. We establish a Wang sequence, which computes

Pseudo-Sylvester domains and skew laurent polynomials over firs

Building on recent work of Jaikin-Zapirain, we provide a homological criterion for a ring to be a pseudo-Sylvester domain, that is, to admit a non-commutative field of fractions over which all stably

References

SHOWING 1-10 OF 34 REFERENCES

Transformation groups and algebraic K-theory

Algebraic K-theory of spaces. In Algebraic and geometric topology (New Brunswick, N.J

  • 1983

On the algebraicK-theory of infinite product categories

L2-Invariants: Theory and Applications to Geometry and K-Theory

0. Introduction.- 1. L2-Betti Numbers.- 2. Novikov-Shubin Invariants.- 3. L2-Torsion.- 4. L2-Invariants of 3-Manifolds.- 5. L2-Invariants of Symmetric Spaces.- 6. L2-Invariants for General Spaces

Higher Algebraic K-Theory

Negative K-theory of derived categories

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.

Split Injectivity of A-Theoretic Assembly Maps

We construct an equivariant coarse homology theory arising from the algebraic $K$-theory of spherical group rings and use this theory to derive split injectivity results for associated assembly

Higher Algebraic K-Theory of Schemes and of Derived Categories

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