On quasianalytic local rings

Artin-Lang property for quasianalytic rings

We prove the Artin-Lang property for some subrings of the ring of smooth function germs at the origin of R2, such rings are for instance unions of quasianalytic Denjoy-Carleman classes. AMS Subject Classification: Prymary 26E10, 13J30; Secondary 14P15.

On Bernstein Classes of Quasianalytic Maps

We study the structure of families of “well approximable” elements of tensor products of Banach spaces including analogs of the classical quasianalytic classes in the sense of Bernstein and Beurling. As in the case of quasianalytic functions, we prove for members of these families variants of the Mazurkiewicz and Markushevich theorems and in some particular cases, if such elements are Banach-va...

On Sums of Squares in Local Rings

Let A be a semilocal ring. We compare the set of positive semidefinite (psd) elements of A and the set of sums of squares in A. For psd f ∈ A, whether f is a sum of squares or not depends only on the behavior of f in an infinitesimal neighborhood of the real zeros of f in Spec A. We apply this observation, first to 1-dimensional local rings, then to 2-dimensional regular semilocal rings. For th...

Convergent Higher Derivations on Local Rings

On Some Local Cohomology Invariants of Local Rings

Let A be a commutative Noetherian local ring containing a field of characteristic p > 0. The integer invariants λi,j(A) have been introduced in an old paper of ours. In this paper we completely describe λd,d(A) where d = dimA in terms of the topology of SpecA.