The Countable Telescope Conjecture arose in the framework of stable homotopy theory, as
a tool conceived to study the chromatic filtration. It turned out, however, to trigger extremely …

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 folklore result …

We prove a modified version of Ravenel's telescope conjecture. It is shown that every
smashing subcategory of the stable homotopy category is generated by a set of maps …

We study a certain monoid of endofunctors of the stable homotopy category that includes
localizations with respect to finite unions of Morava $ K $-theories. We work in an axiomatic …

In this paper, we study the global structure of an algebraic avatar of the derived category of
ind‐coherent sheaves on the moduli stack of formal groups. In analogy with the stable …

We introduce a new topological invariant of a rigidly-compactly generated tensor-
triangulated category and two new notions of support. The first is based on smashing …

We extend the theory of ambidexterity developed by MJ Hopkins and J. Lurie and show that
the $\infty $-categories of $ T (n) $-local spectra are $\infty $-semiadditive for all $ n $, where …

In the stable category of spectra [special characters omitted], the generating hypothesis
([special characters omitted]) is the following conjecture: If f is a map of finite spectra and π∗ …

We discuss the chromatic filtration in stable homotopy theory and its connections with
algebraic K-theory, specifically with some results of Thomason, Mitchell, Waldhausen and …

Following the conventions of algebraists, we will call triangulated subcategories of D*(R)
epaisse if they are full and closed under direct summands. Hopkins' theorem is a beautiful …