Ishan Levy

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.AT2026

Picard groups of quotient ring spectra

Ishan Levy, Guchuan Li, Ningchuan Zhang

We develop tools to study Picard groups of quotients of ring spectra by a finitely generated ideal, which we use to show that $Pic (E_{n} / I) = Z /2$ , where $…

math.AT2025

The spectral Sullivan conjecture

Ishan Levy

We show that any map from an infinite loop space to a $p$ -complete nilpotent finite dimensional space factors canonically through a union of $p$ -adic tori. This is proven via boots…

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…

Dualizable Additive Categories

Picard groups of quotient ring spectra

The spectral Sullivan conjecture

c-structures and trace methods beyond connective rings

$c$ -structures and trace methods beyond connective rings