Topological Hochschild homology of number rings

Lindenstrauss, Ayelet; Madsen, Ib

doi:10.1090/s0002-9947-00-02611-8

Cited by 27 publications

(25 citation statements)

References 21 publications

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“…In [6], Krause-Nikolaus also introduce a descent style spectral sequence to compute the topological Hochschild homology of quotients of DVRs. Their work also recover the main result of Lindenstrauss-Madsen [7] as ours (Corollary 5.19).…”

Section: Relation With Other Worksupporting

confidence: 86%

Topological Cyclic Homology of Local Fields

Liu¹,

Wang²

2020

Preprint

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Section: Relation With Other Worksupporting

confidence: 86%

Topological Cyclic Homology of Local Fields

Liu¹,

Wang²

2020

Preprint

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“…In this section, we again implicitly consider homotopy groups with Z 2 -coefficients. The groups TR 1 q (Z; 2) were evaluated by Bökstedt [3]; see also [23,Thm. 1.1].…”

Section: ⊓ ⊔mentioning

confidence: 99%

On the Whitehead Spectrum of the Circle

Hesselholt

2009

Algebraic Topology

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The seminal work of Waldhausen, Farrell and Jones, Igusa, and Weiss and Williams shows that the homotopy groups in low degrees of the space of homeomorphisms of a closed Riemannian manifold of negative sectional curvature can be expressed as a functor of the fundamental group of the manifold. To determine this functor, however, it remains to determine the homotopy groups of the topological Whitehead spectrum of the circle. The cyclotomic trace of Bökstedt, Hsiang, and Madsen and a theorem of Dundas, in turn, lead to an expression for these homotopy groups in terms of the equivariant homotopy groups of the homotopy fiber of the map from the topological Hochschild T-spectrum of the sphere spectrum to that of the ring of integers induced by the Hurewicz map. We evaluate the latter homotopy groups, and hence, the homotopy groups of the topological Whitehead spectrum of the circle in low degrees.

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“…In the above case ku ( p) behaves like the ring of integers of K U ( p) , and similarly for the connective Adams summand. The result for relative THH corresponds to the one of ordinary rings of integers [18]. In other cases, taking the connective cover does not seem to give good results.…”

Section: Relative Thh Of Ku ( P) As a Commutative -Algebramentioning

confidence: 88%

Towards an understanding of ramified extensions of structured ring spectra

Dundas

Lindenstrauss

Richter

2018

Math. Proc. Camb. Phil. Soc.

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We propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the p-local integers. For the tamely ramified extension of the map from the connective Adams summand to p-local complex topological K-theory we determine the relative topological Hochschild homology and show that it detects the tame ramification of this extension. We show that the complexification map from connective topological real to complex K-theory shows features of a wildly ramified extension. We also determine relative topological Hochschild homology for some quotient maps with commutative quotients.

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Topological Hochschild homology of number rings

Abstract: Abstract. We calculate an explicit formula for the topological Hochschild homology of a discrete valuation ring of characteristic zero with finite residue field. From this we deduce the topological Hochschild homology of global number rings.

Cited by 27 publications

References 21 publications

Topological Cyclic Homology of Local Fields

Topological Cyclic Homology of Local Fields

On the Whitehead Spectrum of the Circle

Towards an understanding of ramified extensions of structured ring spectra

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