835 research outputs found
Gorenstein algebras and Hochschild cohomology
For homomorphism K-->S of commutative rings, where K is Gorenstein and S is
essentially of finite type and flat as a K-module, the property that all
non-trivial fiber rings of K-->S are Gorenstein is characterized in terms of
properties of the cohomology modules Ext_n^{S\otimes_KS}S{S\otimes_KS}.Comment: This is the published version, except for updates to references and
bibliography. Sections 3, 4 and 8 have been removed from the preceding
version, arXiv:0704.3761v2. Substantial generalizations of results in those
sections are proved in our paper with Joseph Lipman and Suresh Nayak,
arXiv:0904.400
Homology of perfect complexes
It is proved that the sum of the Loewy lengths of the homology modules of a
finite free complex F over a local ring R is bounded below by a number
depending only on R. This result uncovers, in the structure of modules of
finite projective dimension, obstructions to realizing R as a closed fiber of
some flat local homomorphism. Other applications include, as special cases,
uniform proofs of known results on free actions of elementary abelian groups
and of tori on finite CW complexes. The arguments use numerical invariants of
objects in general triangulated categories, introduced here and called levels.
They allow one to track, through changes of triangulated categories,
homological invariants like projective dimension, as well as structural
invariants like Loewy length. An intermediate result sharpens, with a new
proof, the New Intersection Theorem for commutative algebras over fields. Under
additional hypotheses on the ring stronger estimates are proved for Loewy
lengths of modules of finite projective dimension.Comment: This version corrects an error in the statement (and proof) of
Theorem 7.4 in the published version of the paper [Adv. Math. 223 (2010)
1731--1781]. These changes do not affect any other results or proofs in the
paper. A corrigendum has been submitted
The theoretical DFT study of electronic structure of thin Si/SiO2 quantum nanodots and nanowires
The atomic and electronic structure of a set of proposed thin (1.6 nm in
diameter) silicon/silica quantum nanodots and nanowires with narrow interface,
as well as parent metastable silicon structures (1.2 nm in diameter), was
studied in cluster and PBC approaches using B3LYP/6-31G* and PW PP LDA
approximations. The total density of states (TDOS) of the smallest
quasispherical silicon quantum dot (Si85) corresponds well to the TDOS of the
bulk silicon. The elongated silicon nanodots and 1D nanowires demonstrate the
metallic nature of the electronic structure. The surface oxidized layer opens
the bandgap in the TDOS of the Si/SiO2 species. The top of the valence band and
the bottom of conductivity band of the particles are formed by the silicon core
derived states. The energy width of the bandgap is determined by the length of
the Si/SiO2 clusters and demonstrates inverse dependence upon the size of the
nanostructures. The theoretical data describes the size confinement effect in
photoluminescence spectra of the silica embedded nanocrystalline silicon with
high accuracy.Comment: 22 pages, 5 figures, 1 tabl
Evolutionary biology studies on the Iris pumila clonal plant: Advantages of a good model system, main findings and directions for further research
Evolutionary studies on the dwarf bearded iris, Iris pumila L., a perennial clonal monocot with hermaphroditic enthomophylous flowers, have been conducted during the last three decades on plants and populations from the Deliblato Sands in Serbia. In this review we discuss the main advantages of this model system that have enabled various studies of several important genetic, ecological, and evolutionary issues at different levels of biological organization (molecular, physiological, anatomical, morphological and population). Based on published research and its resonance in international scientific literature, we present the main findings obtained from these studies, and discuss possible directions for further research
Modern Approaches in Injuries of the Larynx
Introduction: Early diagnosis and proper treatment of laryngeal trauma is of great importance for the patient to prevent the formation of stenosis in a later stage, changes in breathing and voice quality.Material and methods: The covered laryngeal trauma is a relatively rare injury. Its incidence is estimated at 1 in 30,000 visits to emergency rooms.Results: Due to their relatively low frequency and association with other life-threatening injuries, laryngeal trauma often go unrecognized. This is bad because the glottis laryngeal stenosis and insufficiency are the end result of delayed or inadequate treatment of laryngeal trauma.Conclusion: Despite the great variety of these injuries, correct diagnosis and understanding of each case justify the adoption of a standardized method for classifying and treating these injuries. These preconditions will facilitate successful therapy
Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension
Let be a local ring, and let and be finitely generated
-modules such that has finite complete intersection dimension. In this
paper we define and study, under certain conditions, a pairing using the
modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand
diference. We exploit this pairing to examine the number of consecutive
vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all
. Our results recover and improve on most of the known bounds in the
literature, especially when has dimension at most two
(Contravariant) Koszul duality for DG algebras
A DG algebras over a field with connected and
has a unique up to isomorphism DG module with . It is proved
that if is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op}
\equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories
of DG modules with degreewise finite-dimensional homology. It induces an
equivalences of and the category of perfect DG
-modules, and vice-versa. Corresponding statements are proved also
when is simply connected and .Comment: 33 page
- …