Topological Hochschild homology of adic rings
Research output: Book/Report › Ph.D. thesis › Research
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 ←n T(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.
Original language | English |
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Publisher | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
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Number of pages | 93 |
Publication status | Published - 2023 |
ID: 376922748