This paper surveys the recent advances concerning the relations between triangulated (or
derived) categories and their dg enhancements. We explain when some interesting …

In this work we present a new approach to the theory of noncommutative motives and use it
to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work …

The purpose of these four lectures is to provide an introduction to the theory of dg-
categories. There are several possible points of view to present the subject, and my choice …

We define negative K-groups for exact categories and for``derived categories''in the
framework of Frobenius pairs, generalizing definitions of Bass, Karoubi, Carter, Pedersen …

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 …

Schlichting conjectured that the negative K-groups of small abelian categories vanish and
proved this for noetherian abelian categories and for all abelian categories in degree-1-1 …

The new homotopy theory of exact∞-categories is introduced and employed to prove a
Theorem of the Heart for algebraic K-theory (in the sense of Waldhausen). This implies a …

The idea for this book was conceptualized during a research visit to Macquarie University in
the summer of 2017. At first, I was interested in collecting exotic examples of model …

K-THEORY AND DERIVED EQUIVALENCES Page 1 K-THEORY AND DERIVED
EQUIVALENCES DANIEL DUGGER and BROOKE SHIPLEY Abstract We show that if two …

Motivic local systems over a curve in finite characteristic form a countable set endowed with
an action of the absolute Galois group of rational numbers commuting with the Frobenius …