Gross–Hopkins duality

By N. Strickland. 2000

60 citations recorded by the source corpus.

Abstract We give a new and simpler proof of a result of Hopkins and Gross relating Brown-Comenetz duality to Spanier-Whitehead duality in the K(n) -local stable homotopy category.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/15b55f0b54a4a74550abcc0d503097780ad2e944

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In Geometry and Topology

1. Mark Behrens
2. Paul G. Goerss
3. Charles Rezk
4. I. Bobkova
5. M. Mahowald
6. H. Henn
7. M. Hopkins
8. E. Devinatz

In Mathematical Physics

1. Paul G. Goerss
2. Mark Behrens
3. I. Bobkova
4. Charles Rezk
5. M. Mahowald
6. H. Henn
7. M. Hopkins
8. E. Devinatz

Citations in the corpus

• Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups (2004, background): “3) (An identi cation of this sort rst appears in the literature in [30].”
• A resolution of the K(2)-local sphere at the prime 3 (2005, background): “See the remarks before Theorem 20 of [27] for an explanation.”
• Topological resolutions in K(2) ‐local homotopy theory at the prime 2 (2016, background): “es. Furthermore, if E Xis pro-free and concentrated in even degrees, then K(n) X˘=F pn E 0 E X˘=(E X)=m: Remark 1.26. We now come to the Adams-Novikov Spectral Sequence in K(n)- local category. As in [Str00], Proposition 15, this spectral sequence is obtained by the standard cosimplicial cobar compl”
• A modular description of the K(2)-local sphere at the prime 3 (2005, methodology): “Since IK is invertible, we have for any X [46] DX ^ IK ' IKX: Smashing this equation with I 1 K gives DX ' IKX ^ I 1 K : In particular, we may let X be TMF , TMF0(2), or E(2), and then apply Propositions 2.”