Real orientations of Lubin–Tate spectra

Hahn, Jeremy; Shi, XiaoLin Danny

doi:10.1007/s00222-020-00960-z

Cited by 30 publications

(22 citation statements)

References 44 publications

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“…Homotopy coherent versions of this definition have been considered before (e.g. [Lur13], [Spi16], [HS19]). We will however only consider this strict pointset definition, which we will apply in the context of genuine equivariant spectra.…”

Section: Real I-spacesmentioning

confidence: 99%

Real topological Hochschild homology

et al. 2020

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Section: Real I-spacesmentioning

confidence: 99%

Real topological Hochschild homology

et al. 2020

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“…The proof for Theorem 1.8 can be modified to prove Hurewicz images for the homotopy fixed point spectra E hG n . In [HS17], the authors show that the Hurewicz images of ER(n) C2 and E hC2 n are the same. It follows that Theorem 1.8 holds for π * E hC2 n as well.…”

Section: The Proof Of Theorem 15 Requires Us To Analyze the Algebraic...mentioning

confidence: 99%

Hurewicz images of real bordism theory and real Johnson–Wilson theories

Shi

Wang

et al. 2019

Advances in Mathematics

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We show that the Hopf elements, the Kervaire classes, and theκfamily in the stable homotopy groups of spheres are detected by the Hurewicz map from the sphere spectrum to the C 2 -fixed points of the Real bordism spectrum. A subset of these families is detected by the C 2 -fixed points of Real Johnson-Wilson theory ER(n), depending on n. In the proof, we establish an isomorphism between the slice spectral sequence and the C 2 -equivariant May spectral sequence of BP R .

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“…Hyperreal oriented cohomology theories for n > 1 were first applied in the Hill-Hopkins-Ravenel solution to the Kervaire invariant one problem in geometric topology [HHR16]. They have since been applied to study the stable homotopy groups of spheres [HS20,HSWX18,LSWX19], where their fixed points model the fixed points of Lubin-Tate spectra.…”

Section: Motivation and Applicationsmentioning

confidence: 99%

On the parametrized Tate construction

Quigley¹,

Shah²

2021

Preprint

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We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension G of a finite group G by a compact Lie group K, which we call the parametrized Tate construction (−) t G K . Our main theorem establishes the coincidence of three conceptually distinct approaches to its construction when K is also finite: one via recollement theory for the K-free G-family, another via parametrized ambidexterity for G-local systems, and the last via parametrized assembly maps. We also show that (−) t G K uniquely admits the structure of a lax G-symmetric monoidal functor, thereby refining a theorem of Nikolaus and Scholze. Along the way, we apply a theorem of the second author to reprove a result of Ayala-Mazel-Gee-Rozenblyum on reconstructing a genuine G-spectrum from its geometric fixed points; our method of proof further yields a formula for the geometric fixed points of an F -complete G-spectrum for any G-family F . 4 We endow Fun G (B ψ G K, Sp G ) with the pointwise symmetric monoidal structure of Definition A.1. 5 We write this as Ψ K to distinguish it from the spectrum-valued functor of categorical K-fixed points (−) K : Sp G Sp.

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Real orientations of Lubin–Tate spectra

Cited by 30 publications

References 44 publications

Real topological Hochschild homology

Real topological Hochschild homology

Hurewicz images of real bordism theory and real Johnson–Wilson theories

On the parametrized Tate construction

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