This book provides an introduction to modern homotopy theory through the lens of higher
categories after Joyal and Lurie, giving access to methods used at the forefront of research …

We prove that the Witt vector affine Grassmannian, which parametrizes W (k)-lattices in W (k)
1 p^ n W (k) 1 pn for a perfect field k of characteristic p, is representable by an ind-(perfect …

In this paper we establish a universal characterization of higher algebraic K–theory in the
setting of small stable∞–categories. Specifically, we prove that connective algebraic K …

Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as
defined by Dress. We show that they can be described as excisive functors on a suitable∞ …

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 show that Lubin--Tate theories attached to algebraically closed fields are characterized
among $ T (n) $-local $\mathbb {E} _ {\infty} $-rings as those that satisfy an analogue of …

We prove that the∞-category of MGL-modules over any scheme is equivalent to the∞-
category of motivic spectra with finite syntomic transfers. Using the recognition principle for …

We propose a categorification of the Chern character that refines earlier work of Toën and
Vezzosi and of Ganter and Kapranov. If X is an algebraic stack, our categorified Chern …

Schlichting conjectured that the negative K-groups of small abelian categories vanish and
proved this for noetherian abelian categories and for all abelian categories in degree-1-1 …

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 …