Some recent advances in topological Hochschild homology - Mathew - 2022 - Bulletin of the
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Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

The connective topological modular forms spectrum, $ tmf $, is in a sense initial among
elliptic spectra, and as such is an important link between the homotopy groups of spheres …

Redshift and multiplication for truncated Brown–Peterson spectra Page 1 Annals of
Mathematics 196 (2022), 1277–1351 https://doi.org/10.4007/annals.2022.196.3.6 Redshift and …

We prove that $ T (n+ 1) $-localized algebraic $ K $-theory satisfies descent for $\pi $-finite $
p $-group actions on stable $\infty $-categories of chromatic height up to $ n $, extending a …

For a prime number $ p $ and a $ p $-quasisyntomic commutative ring $ R $, Bhatt--Morrow--
Scholze defined motivic filtrations on the $ p $-completions of $\mathrm {THH}(R),\mathrm …

We prove that Waldhausen-theory, when extended to a very general class of
quasicategories, can be described as a Goodwillie differential. In particular,-theory spaces …

To set the scene, we begin here by reviewing basics of homotopy theory via model category
theory [Quillen (1967)](review in [Hovey (1999)][Hirschhorn (2003)][Lurie (2009a), A. 2]) and …

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 …

At each prime $ p $ and height $ n+ 1\ge 2$, we prove that the telescopic and chromatic
localizations of spectra differ. Specifically, for $\mathbb {Z} $ acting by Adams operations on …