645 research outputs found
Nonvanishing cohomology and classes of Gorenstein rings
We give counterexamples to the following conjecture of Auslander: given a
finitely generated module over an Artin algebra , there exists a
positive integer such that for all finitely generated -modules
, if \Ext_{\Lambda}^i(M,N)=0 for all , then
\Ext_{\Lambda}^i(M,N)=0 for all . Some of our examples moreover
yield homologically defined classes of commutative local rings strictly between
the class of local complete intersections and the class of local Gorenstein
rings.Comment: 16 page
Free resolutions over short local rings
The structure of minimal free resolutions of finite modules M over
commutative local rings (R,m,k) with m^3=0 and rank_k(m^2) < rank_k(m/m^2)is
studied. It is proved that over generic R every M has a Koszul syzygy module.
Explicit families of Koszul modules are identified. When R is Gorenstein the
non-Koszul modules are classified. Structure theorems are established for the
graded k-algebra Ext_R(k,k) and its graded module Ext_R(M,k).Comment: 17 pages; number of minor changes. This article will appear in the
Journal of the London Math. So
Magnetic response of nonmagnetic impurities in cuprates
A theory of the local magnetic response of a nonmagnetic impurity in a doped
antiferromagnet, as relevant to the normal state in cuprates, is presented. It
is based on the assumption of the overdamped collective mode in the bulk system
and on the evidence, that equal-time spin correlations are only weakly
renormalized in the vicinity of the impurity. The theory relates the Kondo-like
behavior of the local susceptibility to the anomalous temperature dependence of
the bulk magnetic susceptibility, where the observed increase of the Kondo
temperature with doping reflects the crossover to the Fermi liquid regime and
the spatial distribution of the magnetization is given by bulk
antiferromagnetic correlations.Comment: 5 pages, 3 figure
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