The First Cohomology Group of the Generalized Morava Stabilizer Algebra
نویسندگان
چکیده
There exists a p-local spectrum T (m) with BP∗(T (m))= BP∗[t1, . . . , tm]. Its Adams-Novikov E2-term is isomorphic to ExtΓ(m+1)(BP∗, BP∗), where Γ(m+ 1) = BP∗(BP )/ (t1, . . . , tm) = BP∗[tm+1, tm+2, . . . ]. In this paper we determine the groups ExtΓ(m+1)(BP∗, v −1 n BP∗/In) for all m,n > 0. Its rank ranges from n + 1 to n2 depending on the value of m.
منابع مشابه
Products of Greek Letter Elements Dug up from the Third Morava Stabilizer Algebra
In [3], Oka and the second author considered the cohomology of the second Morava stabilizer algebra to study nontriviality of the products of beta elements of the stable homotopy groups of spheres. In this paper, we use the cohomology of the third Morava stabilizer algebra to find nontrivial products of Greek letters of the stable homotopy groups of spheres: α1γt, β2γt, 〈α1, α1, β p/p〉γtβ1 and ...
متن کاملMODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS
Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations from the triangular Banach algebraof t...
متن کاملThe Cohomology of the Height Four Morava Stabilizer Group at Large Primes
This is an announcement of some new computational methods in stable homotopy theory, in particular, methods for using the cohomology of small-height Morava stabilizer groups to compute the cohomology of large-height Morava stabilizer groups. As an application, the cohomology of the height four Morava stabilizer group is computed at large primes (its rank turns out to be 3440). Consequently we a...
متن کاملThe First Cohomology Group of the Generalized Morava Stabilizer Algebra (draft Version)
There are p-local spectra T (m) with BP∗(T (m)) = BP∗[t1, . . . , tm]. Its Adams-Novikov E2-term is isomorphic to ExtΓ(m+1)(BP∗, BP∗), where Γ(m + 1) = BP∗(BP )/ (t1, . . . , tm) = BP∗[tm+1, tm+2, . . . ]. In this paper we determine the groups ExtΓ(m+1)(BP∗, v −1 n BP∗/In) for all m, n > 0. Its rank ranges from 2n + 1 to n2 depending on the value of m.
متن کاملComparison of Morava E-theories
In this note 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 Ecohomology group with action of the (n + 1)st Morava stabilizer group.
متن کامل