3 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.AT2025
The spectral Sullivan conjecture
Ishan Levy
We show that any map from an infinite loop space to a -complete nilpotent finite dimensional space factors canonically through a union of -adic tori. This is proven via boots…
math.KT2025
-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…