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 …

We define Grothendieck-Witt spectra in the setting of Poincaré-categories and show that
they fit into an extension with a K-and an L-theoretic part. As consequences, we deduce …

We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …

We show that every sheaf on the site of smooth manifolds with values in a stable (∞, 1)(∞,
1)-category (like spectra or chain complexes) gives rise to a “differential cohomology …

Following ideas of Lurie, we give a general construction of equivariant elliptic cohomology
without restriction to characteristic zero. Specializing to the universal elliptic curve we obtain …

We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This
is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of …

Let A→ B be a G-Galois extension of rings, or more generally of E∞-ring spectra in the
sense of Rognes. A basic question in algebraic K-theory asks how close the map K (A)→ K …

Many homotopy-coherent algebraic structures can be described by Segal-type limit
conditions determined by an “algebraic pattern”, by which we mean an∞-category equipped …

We study the Yoneda lemma for arbitrary simplicial spaces. We do that by introducing left
fibrations of simplicial spaces and studying their associated model structure, the covariant …

We develop a general theory of higher semiadditive Fourier transforms that includes both
the classical discrete Fourier transform for finite abelian groups at height-modules [-12pc] …