Tobias Barthel

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20172025

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math.AT2024

The spectrum of excisive functors

Gregory Arone, Tobias Barthel, Drew Heard +1

We prove a thick subcategory theorem for the category of $d$ -excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=…

math.AT2024

Profinite equivariant spectra and their tensor-triangular geometry

Scott Balchin, David Barnes, Tobias Barthel

We study the tensor-triangular geometry of the category of equivariant $G$ -spectra for $G$ a profinite group, $Sp_{G}$ . Our starting point is the construction of a ``continu…

math.AT2023

Prismatic decompositions and rational $G$ -spectra

Scott Balchin, Tobias Barthel, J. P. C. Greenlees

We study the tensor-triangular geometry of the category of rational $G$ -spectra for a compact Lie group $G$ . In particular, we prove that this category can be naturally decomposed…

math.AT2017

On the comparison of stable and unstable $p$ -completion

Tobias Barthel, A. K. Bousfield

In this note we show that a $p$ -complete nilpotent space $X$ has a $p$ -complete suspension spectrum if and only if its homotopy groups $π_{*} X$ are bounded $p$ -torsion. In contrast,…

The spectrum of excisive functors

Profinite equivariant spectra and their tensor-triangular geometry

Prismatic decompositions and rational G-spectra

On the comparison of stable and unstable p-completion

Prismatic decompositions and rational $G$ -spectra

On the comparison of stable and unstable $p$ -completion