Work

Comparing Dualities in the $K(n)$-local Category

Year: 2020

Type: book

Abstract: In their work on the period map and the dualizing sheaf for Lubin-Tate space, Gross and the second author wrote down an equivalence between the Spanier-Whitehead and Brown-Comenetz duals of certain type $n$-complexes in the $K(n)$-local category at large primes. In the culture of the time, these results were accessible to educated readers, but this seems no longer to be the case; therefore, in this note we give the details. Because we are at large primes, the key result is algebraic: in the Picard group of Lubin-Tate space, two important invertible sheaves become isomorphic modulo $p$.

Source: Digital Access to Scholarship at Harvard (DASH) (Harvard University)

DOI: 10.48550/arxiv.2011.02011

Authors: Goerss, Paul G., Hopkins, Michael J.

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: Isaac Newton Institute for Mathematical Sciences, G4421442999, G4947591155, G7000731051, New Frontiers in Homotopy Theory

OpenAlex ID: W3097862153

FWCI: 0.288

Cites: 23

Cited by: 4

Related to: 20