Topological Hochschild homology of adic rings
Research output: Book/Report › Ph.D. thesis › Research
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Topological Hochschild homology of adic rings. / Cordova Fedeli, Adriano.
Department of Mathematical Sciences, Faculty of Science, University of Copenhagen, 2023. 93 p.Research output: Book/Report › Ph.D. thesis › Research
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TY - BOOK
T1 - Topological Hochschild homology of adic rings
AU - Cordova Fedeli, Adriano
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
M3 - Ph.D. thesis
BT - Topological Hochschild homology of adic rings
PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen
ER -
ID: 376922748