Abstract. In this note we study a certain formal group law over a complete discrete valuation ring F[[u n−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 H n−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 S n−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 S n−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.

No abstract

We give descriptions of the moduli of representations with Borel mold for free monoids as fibre bundles over the configuration spaces. By using the associated Serre spectral sequences, we study the cohomology rings of the moduli. Also we calculate the virtual Hodge polynomials of them.

We show that the nth Morava E-cohomology group of a finite spectrum with action of the nth Morava stabilizer group can be recovered from the (n + 1)st Morava E-cohomology group with action of the (n + 1)st Morava stabilizer group.

No abstract