Refined THH Over ku and Habiro Cohomology

Explore advanced topics in arithmetic geometry through this mathematical lecture examining refined topological Hochschild homology (THH) over ku and its connection to Habiro cohomology. Learn how Efimov's theorem on the rigidity of localizing motives enables the construction of refinements of topological Hochschild homology and its variants, building on observations by Efimov and Scholze. Discover how refined THH over ku leads to a new cohomology theory for varieties over rational numbers, with detailed calculations demonstrating its applications. Understand how this new cohomology theory provides insights into Scholze's Habiro stack and offers the desired modification at the Hodge-Tate point that current constructions lack. Gain exposure to cutting-edge research connecting topological methods with arithmetic geometry, presented by Ferdinand Wagner from MPIM/University of Bonn as part of the Joint IAS/PU Arithmetic Geometry seminar series.