PhD Defense Adriano Cordova Fedeli

Title: Topological Hochschild homology of adic rings

Abstract:

Let R be an E∞-ring, and let I ⊂ π0R be a finitely generated ideal such that R is complete along I. This thesis studies localizing invariants arising from pairs of the form (R, I). Precisely, the pair (R, I) gives rise to a category NucR, the category of nuclear R-modules: this category contains the usual category of R-modules, as well as many I-complete R-modules with continuous maps between them. We then study localizing invariants applied to such categories. In this context, a localizing invariant T is said to be continuous if T(NucR) = lim ←−nT(RIn). Efimov proved that algebraic K-theory is continuous. The main result of this thesis builds from the continuity of K-theory to prove the same for topological cyclic and Hochschild homology.

Thesis for download

Advisor: Dustin Clausen, University of Copenhagen & IHES

Assesment committee:

Fabien Pazuki (chair), University of Copenhagen
Alexander Efimov,  Steklov Mathematical Institute of Russian Academy of Sciences
Arthur César le Bras, University of Strasbourg 

Join online:

https://ucph-ku.zoom.us/j/68738157119?pwd=Mjcxd1BNL29qSzUrdzQxbGxIdEg1dz09
Zoom ID: 687 3815 7119
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