7 papers
Transfer ideals and torsion in the Morava -theory of abelian groups
Tobias Barthel, Nathaniel Stapleton
Let be a finite abelian group of rank at least . We show that , the quotient of the Morava -cohomology of by the ideal generated by the image of t…
Local Gorenstein duality for cochains on spaces
Tobias Barthel, Natalia Castellana, Drew Heard +1
We investigate when a commutative ring spectrum satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to d…
Monochromatic homotopy theory is asymptotically algebraic
Tobias Barthel, Tomer M. Schlank, Nathaniel Stapleton
In previous work, we used an -categorical version of ultraproducts to show that, for a fixed height , the symmetric monoidal -categories of -local spect…
A short introduction to the telescope and chromatic splitting conjectures
Tobias Barthel
In this note, we give a brief overview of the telescope conjecture and the chromatic splitting conjecture in stable homotopy theory. In particular, we provide a proof of the folklo…
Chromatic structures in stable homotopy theory
Tobias Barthel, Agnès Beaudry
In this survey, we review how the global structure of the stable homotopy category gives rise to the chromatic filtration. We then discuss computational tools used in the study of…
Excellent rings in transchromatic homotopy theory
Tobias Barthel, Nathaniel Stapleton
The purpose of this note is to verify that several basic rings appearing in transchromatic homotopy theory are Noetherian excellent normal domains and thus amenable to standard tec…