33 citations · 86 across the 18 of their papers we have counts for
22 papers
Dualizable Additive Categories
Ishan Levy, Jiacheng Liang, Vladimir Sosnilo
We develop a comprehensive theory of dualizable additive categories. We provide several equivalent characterizations, notably identifying them as separated Grothendieck prestable c…
-structures and trace methods beyond connective rings
Ishan Levy, Vladimir Sosnilo
We introduce the notion of a -category, which is a kind of category whose behaviour is controlled by connective ring spectra. More precisely, any -category admits a finite st…
Every motive is the motive of a stable -category
Maxime Ramzi, Vladimir Sosnilo, Christoph Winges
We define a class of motivic equivalences of small stable -categories and show that the Dwyer--Kan localization functor $\mathrm{Cat}^{\mathrm{perf}}_\in…
On filtered algebraic -theory of stacks I: characteristic zero
Elden Elmanto, Dmitry Kubrak, Vladimir Sosnilo
Given a compact Lie group acting on a space , the classical Atiyah-Segal completion theorem identifies topological -theory of the homotopy quotient with an explicit…
Every spectrum is the K-theory of a stable -category
Maxime Ramzi, Vladimir Sosnilo, Christoph Winges
We prove that any spectrum is equivalent to the nonconnective K-theory of a stable -category. We use these results to construct a stable -category wit…
-invariance of localizing invariants
Vladimir Sosnilo
Weibel proved that -inverted K-theory is -invariant on -schemes and K-theory with -coefficients is -invariant on $\mathbb…