On graded rings with finiteness conditions

ON FINITENESS OF PRIME IDEALS IN NORMED RINGS

In a commutative Noetherian local complex normed algebra which is complete in its M-adic metric there are only finitely many closed prime ideals.

Schur-finiteness in Λ-rings

We introduce the notion of a Schur-finite element in a λ-ring. Since the beginning of algebraic K-theory in [G57], the splitting principle has proven invaluable for working with λ-operations. Unfortunately, this principle does not seem to hold in some recent applications, such as the K-theory of motives. The main goal of this paper is to introduce the subring of Schur-finite elements of any λ-r...

Finiteness of Unramified Deformation Rings

We prove that the universal unramified deformation ring R of a continuous Galois representation ρ : GF+ → GLn(k) (for a totally real field F and finite field k) is finite over O = W (k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring R is finite over the local deformation ring R.

Results on Finiteness of Graded Local Cohomology Modules

Let R = ⊕ n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R− module. In this paper we show that if R0 is a local ring of dimension one, then H i R+(H 1 m0R (M)) is Artinian for each i ∈ N0. Let f be the least integer such that H i m0R(M) is not finitely generated graded R−module. In this case, we prove that ΓR+(...

On Associated Graded Rings of Normal Ideals