V. Sosnilo

collaborators

4 papers

math.AT2026

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…

math.KT2025

$c$ -structures and trace methods beyond connective rings

Ishan Levy, Vladimir Sosnilo

We introduce the notion of a $c$ -category, which is a kind of category whose behaviour is controlled by connective ring spectra. More precisely, any $c$ -category admits a finite st…

math.KT2025

Every motive is the motive of a stable $\infty$ -category

Maxime Ramzi, Vladimir Sosnilo, Christoph Winges

We define a class of motivic equivalences of small stable $\infty$ -categories $W_{mot}$ and show that the Dwyer--Kan localization functor $\mathrm{Cat}^{\mathrm{perf}}_\in…

math.AG2025

On filtered algebraic $K$ -theory of stacks I: characteristic zero

Elden Elmanto, Dmitry Kubrak, Vladimir Sosnilo

Given a compact Lie group $G$ acting on a space $X$ , the classical Atiyah-Segal completion theorem identifies topological $K$ -theory of the homotopy quotient $X / G$ with an explicit…

Dualizable Additive Categories

c-structures and trace methods beyond connective rings

Every motive is the motive of a stable ∞-category

On filtered algebraic K-theory of stacks I: characteristic zero

$c$ -structures and trace methods beyond connective rings

Every motive is the motive of a stable $\infty$ -category

On filtered algebraic $K$ -theory of stacks I: characteristic zero