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 …

Hodge theory, since its appearance in complex analysis, has long become one of the most
useful tools in complex algebraic geometry. At the core of its algebraic applications lies a …

Publisher Summary This chapter discusses the aspects of Symm, which relate directly to the
Witt vector constructions and their properties. The Witt vector construction is a very beautiful …

We construct and study a $ t $-structure on $ p $-typical cyclotomic spectra and explain how
to recover crystalline cohomology of smooth schemes over perfect fields using this $ t …

We provide foundations for dealing with the equivariant structure of" smash powers" of
commutative orthogonal ring spectra. The category of commutative orthogonal ring spectra …

Topological Hochschild homology (THH) of a “ring up to homotopy” has, after its existence
and even some calculations had been conjectured by Goodwillie in the 1980's, appeared in …

These are lecture notes for series of talks given by the second author in Copenhagen and
Bloomington. Most of the results are based on the paper [NS17]. We also discuss the …

We prove that the Farrell–Jones assembly map for connective algebraic K-theory is
rationally injective, under mild homological finiteness conditions on the group and assuming …

We define twisted Hochschild homology for Green functors. This construction is the
algebraic analogue of the relative topological Hochschild homology THH C n (−), and under …