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 …

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

To any pullback square of ring spectra we associate a new ring spectrum and use it to
describe the failure of excision in algebraic K-theory. The construction of this new ring …

We prove that the rank of the cohomology of a closed symplectic manifold with coefficients in
a field of characteristic $ p $ is smaller than the number of periodic orbits of any non …

Given a henselian pair $(R, I) $ of commutative rings, we show that the relative $ K $-theory
and relative topological cyclic homology with finite coefficients are identified via the …

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 …

This work is dedicated to the construction of a new motivic homotopy theory for (log)
schemes, generalizing Morel-Voevodsky's (un) stable $\mathbb {A}^ 1$-homotopy category …

We describe a comparison between pretriangulated differential graded categories and
certain stable infinity categories. Specifically, we use a model category structure on …

This paper incorporates the theory of Hochschild homology into our program on log motives.
We discuss a geometric definition of logarithmic Hochschild homology of animated pre-log …

This paper interprets Hesselholt and Madsen's real topological Hochschild homology functor
THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality …