On degeneration of one-dimensional formal group laws and applications to stable homotopy theory

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this note we study a certain formal group law over a complete discrete valuation ring F[un-1] of characteristic p > 0 which is of height n over the closed point and of height n - 1 over the generic point. By adjoining all coefficients of an isomorphism between the formal group law on the generic point and the Honda group law Hn-1 of height n - 1, we get a Galois extension of the quotient field of the discrete valuation ring with Galois group isomorphic to the automorphism group Sn-1 of H n-1. We show that the automorphism group Sn of the formal group over the closed point acts on the quotient field, lifting to an action on the Galois extension which commutes with the action of Galois group. We use this to construct a ring homomorphism from the cohomology of Sn-1 to the cohomology of Sn with coefficients in the quotient field. Applications of these results in stable homotopy theory and relation to the chromatic splitting conjecture are discussed.

Original languageEnglish
Pages (from-to)1037-1077
Number of pages41
JournalAmerican Journal of Mathematics
Volume125
Issue number5
Publication statusPublished - Oct 2003
Externally publishedYes

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Formal Group Law
Stable Homotopy
Homotopy Theory
Degeneration
Quotient
Valuation Ring
Galois Extension
Galois group
Automorphism Group
Cohomology
Formal Group
Closed
Coefficient
Commute
Homomorphism
Isomorphism
Isomorphic
Ring

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On degeneration of one-dimensional formal group laws and applications to stable homotopy theory. / Torii, Takeshi.

In: American Journal of Mathematics, Vol. 125, No. 5, 10.2003, p. 1037-1077.

Research output: Contribution to journalArticle

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