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

The author introduces the notion of a Galois extension of commutative $ S $-algebras ($
E_\infty $ ring spectra), often localized with respect to a fixed homology theory. There are …

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 …

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 …

Topological cyclic homology is a manifestation of Waldhausen's vision that the cyclic theory
of Connes and Tsygan should be developed with the initial ring S of higher algebra as base …

Let A be an A∞ ring spectrum. We use the description from our preprint [math. AT/0612165]
of the cyclic bar and cobar construction to give a direct definition of topological Hochschild …

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 …

In this article, we study the topological Hochschild homology of $\mathbf {E} _3 $-forms of
truncated Brown-Peterson spectra, taken relative to certain Thom spectra $ X (p^ n) …

We compute the mod $(p, v_1) $ and mod $(2,\eta, v_1) $$\mathrm {THH} $ of many variants
of the image-of-$ J $ spectrum. In particular, we do this for $ j_ {\zeta} $, whose $\mathrm …