Alexander Efimov: On the K-Theory of Large Triangulated Categories

Explore the intricacies of K-theory in large triangulated categories through this 44-minute lecture by Alexander Efimov, presented by the International Mathematical Union. Delve into key concepts such as Grothendieck groups, categorical localization, and higher algebraic K-theory. Examine the compatibility of definitions and the motivation behind continuous K-theory. Investigate presentable cocomplete categories and dualizable DG categories, including equivalent definitions of dualizability. Learn about the continuous K-theory of nuclear modules through direct computation, and discover practical applications in the field of almost mathematics. Gain a deeper understanding of negative K-theory and K-theory spectra as you navigate this comprehensive exploration of advanced mathematical concepts.

Intro
Grothendieck groups
Compatibility of definitions
Categorical localization
Higher algebraic K-theory
Negative K-theory
K-theory spectra
Motivation for continuous K-theory
Presentable cocomplete categories
Dualizable DG categories
Equivalent definitions of dualizability
Example: almost mathematics
Continuous K-theory of nuclear modules
Direct computation