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 continue to study the logarithmic prismatic cohomology defined by the first author, and
complete the proof of the de Rham comparison and\'etale comparison generalizing those of …

We present a general homotopical analysis of structured diagram spaces and discuss the
relation to symmetric spectra. The main motivating examples are the I-spaces, which are …

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 …

The cohomology theory known as Tmf Tmf, for “topological modular forms,” is a universal
object mapping out to elliptic cohomology theories, and its coefficient ring is closely …

This work is the first in a series laying the foundations of derived geometry in the $ C^{\infty}
$ setting, and providing tools for the construction and study of moduli spaces of solutions of …

In this paper we compute the topological Hochschild homology of quotients of discrete
valuation rings (DVRs). Along the way we give a short argument for Bökstedt periodicity and …

Abstract Inspired by Bhatt–Morrow–Scholze's work on, we define Nygaard-completed log
prismatic cohomology based on log topological Hochschild homology via filtrations on log …

We prove that (logarithmic) prismatic and (logarithmic) syntomic cohomology are
representable in the category of logarithmic motives. As an application, we obtain Gysin …

Working in the context of symmetric spectra, we describe and study a homotopy completion
tower for algebras and left modules over operads in the category of modules over a …