8 citations · 29 across the 18 of their papers we have counts for
22 papers
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…
-theory of endomorphisms, the -trace, and zeta functions
Jonathan A. Campbell, John A. Lind, Cary Malkiewich +2
We show that the characteristic polynomial and the Lefschetz zeta function are manifestations of the trace map from the -theory of endomorphisms to topological restriction homol…
Spectral Waldhausen categories, the -construction, and the Dennis trace
Jonathan A. Campbell, John A. Lind, Cary Malkiewich +2
We give an explicit point-set construction of the Dennis trace map from the -theory of endomorphisms to topological Hochschild homology $\mathrm{THH…
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 $…
Splittings and calculational techniques for higher THH
Irina Bobkova, Eva Höning, Ayelet Lindenstrauss +3
Tensoring finite pointed simplicial sets with commutative ring spectra yields important homology theories such as (higher) topological Hochschild homology and torus homology. We pr…
Derived -adic zeta functions
Jonathan Campbell, Jesse Wolfson, Inna Zakharevich
We lift the classical Hasse--Weil zeta function of varieties over a finite field to a map of spectra with domain the Grothendieck spectrum of varieties constructed by Campbell and…
Relative Loday constructions and applications to higher THH-calculations
Gemma Halliwell, Eva Höning, Ayelet Lindenstrauss +2
We define a relative version of the Loday construction for a sequence of commutative S-algebras and a pointed simplicial subset . We us…
The homotopy theory of equivariant posets
J. P. May, Marc Stephan, Inna Zakharevich
Let be a discrete group. We prove that the category of -posets admits a model structure that is Quillen equivalent to the standard model structure on -spaces. As is alrea…
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.
Extending to a model structure is not a first-order property
Jean-Marie Droz, Inna Zakharevich
Let be a finitely bicomplete category and a subcategory. We prove that the existence of a model structure on with as subcate…
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…
On the higher topological Hochschild homology of and commutative -group algebras
Irina Bobkova, Ayelet Lindenstrauss, Kate Poirier +2
We extend Torleif Veen's calculation of higher topological Hochschild homology from to for odd, and from to $n\l…
Model categories with simple homotopy categories
Jean-Marie Droz, Inna Zakharevich
In the present article, we describe constructions of model structures on general bicomplete categories. We are motivated by the following question: given a category w…
Simplicial Polytope Complexes and Deloopings of -theory
Inna Zakharevich
This paper is a continuation of our previous work in which we defined the notion of a polytope complex and its -theory. In this paper we produce formulas for the delooping of a…
Scissors Congruence as K-theory
Inna Zakharevich
Scissors congruence groups have traditionally been expressed algebraically in terms of group homology. We give an alternate construction of these groups by producing them as the $0…