Topological cyclic homology is a refinement of Connes–Tsygan's cyclic homology which
was introduced by Bökstedt–Hsiang–Madsen in 1993 as an approximation to algebraic K …

The stable homotopy category, much studied by algebraic topologists, is a closed symmetric
monoidal category. For many years, however, there has been no well-behaved closed …

Working in the category of based spaces, we give the basic theory of diagram spaces and
diagram spectra. These are functors for a suitable small topological category. When is …

A stable model category is a setting for homotopy theory where the suspension functor is
invertible. The prototypical examples are the category of spectra in the sense of stable …

We give two general constructions for the passage from unstable to stable homotopy that
apply to the known example of topological spaces, but also to new situations, such as the A …

Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

We show that the homotopy theory of differential graded algebras coincides with the
homotopy theory of HZ-algebra spectra. Namely, we construct Quillen equivalences …

This is an expository paper on homotopy colimits and homotopy limits. These are
constructions which should arguably be in the toolkit of every modern algebraic topologist …

We construct localization cofibration sequences for the topological Hochschild homology
(THH) and topological cyclic homology (TC) of small spectral categories. Using a global …

We apply the ideas of derived algebraic geometry and topological field theory to the
representation theory of reductive groups. Our focus is the Hecke category of Borel …