Algebraic K-Theory and Descent for Blow-Ups - Lecture 1
Explore the intricacies of algebraic K-theory and descent for blow-ups in this lecture from the Hausdorff Trimester Program on K-Theory and Related Fields. Delve into the importance of special cases of descent along blow-ups for calculating K-groups, including Thomason's proof of descent for blow-ups in regular centers. Examine the challenges of general descent for K-theory of blow-ups and discover M. Morrow's potential solution using pro-K-groups of infinitesimal thickenings. Learn about the proof of pro-descent for all blow-ups of noetherian schemes and its implications for Weibel's conjecture on the vanishing of negative K-groups. Gain insights from the joint work of Moritz Kerz, F. Strunk, and G. Tamme in this comprehensive 1-hour and 8-minute lecture on advanced topics in algebraic geometry and K-theory.