Let n be any positive integer and p any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with abutment π∗(LK(n)(X)) and E2-term equal to the continuous cohomology of Gn, the extended Morava stabilizer group, with coefficients in a certain discrete Gn-module that is built from various homotopy fixed point spect...

We compute the PSL(2, N)-module structure of the Riemann-Roch space L(D), where D is an invariant non-special divisor on the modular curve X(N), with N ≥ 7 prime. This depends on a computation of the ramification module, which we give explicitly. These results hold for characteristic p if X(N) has good reduction mod p and p does not divide the order of PSL(2, N). We give as examples the cases N...

Abstract. We show that for any prime number l > 2 the minus class group of the field of the l-th roots of unity Qp(ζl) admits a finite free resolution of length 1 as a module over the ring Ẑ[G]/(1 + ι). Here ι denotes complex conjugation in G = Gal(Qp(ζl)/Qp) ∼= (Z/lZ)∗. Moreover, for the primes l ≤ 509 we show that the minus class group is cyclic as a module over this ring. For these primes we...

In the study of Lie powers of a module V in prime characteristic p, a basic role is played by certain modules Bn introduced by Bryant and Schocker. The isomorphism types of the Bn are not fully understood, but these modules fall into infinite families {Bk,Bpk,Bp2k, . . .}, one family B(k) for each positive integer k not divisible by p, and there is a recursive formula for the modules within B(k...

Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.

We show here how to construct bases of the Z-module Int(P,Z) of polynomials that are integer-valued on the prime numbers together with their finite divided difference, that is, Int(P,Z) = { f ∈ Q[x] | ∀p, q ∈ P f(p) ∈ Z and f(p)− f(q) p− q ∈ Z } .

For a Noetherian local ring, the prime ideals in the singular locus completely determine the category of finitely generated modules up to direct summands, extensions and syzygies. From this some simple homological criteria are derived for testing whether an arbitrary module has finite projective dimension.

We determine all nite groups G which admit a subgroup K of index p a ; p a prime, under the assumption that G has an irreducible and faithful GF (p)-module of dimension at most a. As an application to the theory of permutation groups we determine the maximal transitive subgroups of the primitive aane permutation groups.

The goal of this paper is to give characterizations of minimal primary decompositions and radicals of submodules of any finitely generated module over a PID. To do this, we first consider free modules of finite rank and we characterize prime, primary and maximal submodules as well as minimal primary decompositions and radicals.

We consider the polynomial algebra H∗(CP∞ ×CP∞;Fp) as a module over the mod p Steenrod algebra, A(p), p being an odd prime. We give a minimal set of generators consisting of monomials and characterise all such ‘monomial bases’.