8 citations · 29 across the 18 of their papers we have counts for
11 papers · 1 filter
A stable rank filtration on direct sum -theory
Jonathan Campbell, Alexander Kupers, Inna Zakharevich
In the literature, there are two standard rank filtrations on -theory: an ``unstable'' one which is traditionally defined through the homology of , and a ``stable'' one wh…
Algebraic -theory for squares categories
Jonathan Campbell, Josefien Kuijper, Mona Merling +1
In this paper we introduce a new formalism for -theory, called squares -theory. This formalism allows us to simultaneously generalize the usual three-term relation $[B] = [A]…
A trace map on higher scissors congruence groups
Anna Marie Bohmann, Teena Gerhardt, Cary Malkiewich +2
Cut-and-paste -theory has recently emerged as an important variant of higher algebraic -theory. However, many of the powerful tools used to study classical higher algebraic $…
-Ring structures on the -theory of assemblers and point counting
Inna Zakharevich
We construct a monoidal structure on the category of assemblers. As an application of this, we construct a derived local zeta-function which takes a variety over a finite field to…
Hilbert's third problem and a conjecture of Goncharov
Jonathan Campbell, Inna Zakharevich
In this paper we reduce the generalized Hilbert's third problem about Dehn invariants and scissors congruence classes to the injectivity of certain Chern--Simons invariants. We als…
Devissage and Localization for the Grothendieck Spectrum of Varieties
Jonathan A. Campbell, Inna Zakharevich
We introduce a new perspective on the -theory of exact categories via the notion of a CGW-category. CGW-categories are a generalization of exact categories that admit a Qullen $…
Principal ideals in mod- Milnor -theory
Charles Weibel, Inna Zakharevich
Fix a symbol in the mod- Milnor -theory of a field , and a norm variety for . We show that the ideal generated by is…
The annihilator of the Lefschetz motive
Inna Zakharevich
In this paper we study a spectrum such that is the Grothendieck ring of varieties and such that the higher homotopy groups contain more ge…
On of an assembler
Inna Zakharevich
This paper contains a construction of generators and partial relations for of a simplicial Waldhausen category where cofiber sequences split up to weak equivalence. The main…
The category of Waldhausen categories as a closed multicategory
Inna Zakharevich
This paper works out in detail the closed multicategory structure of the category of Waldhausen categories.
The -theory of assemblers
Inna Zakharevich
In this paper we introduce the notion of an assembler, which formally encodes "cutting and pasting" data. An assembler has an associated -theory spectrum, in which is the…