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Topic: Quasi-isomorphism

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Citations: Lecture Notes in Math - Hartshorne, of, varieties (ResearchIndex) ....2 Z. quasi isomorphism is a morphism ff such that H n (ff) is an isomorphism for all n; we indicate quasi isomorphisms by, while = is our notation for isomorphisms of complexes (and thereby of modules) 1.2) Derived functors. , is denoted by D(R) Isomorphisms in D(R) are labeled with (since a morphism of complexes is a quasi isomorphism if and only if its image in D(R) is an isomorphism, no notational confusion arises) We use to denote isomorphisms up to translation; in particular, H i (M) 0 for i 6= n,. An R complex D is said to be dualizing for R if the homothety morphism D : R RHomR (D; D) is an isomorphism, and D 2 I f (R) We record some important properties of dualizing complexes citeseer.ist.psu.edu /context/918773/0

Volume 24, Number 1, 1998 In particular it follows from Künzi's [8] proofs that each totally bounded locally quiet quasi-uniform space is uniform, and recently Déak [10] observed that even each totally bounded Cauchy quasi-uniformity is a uniformity. We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity. The main result: every free monoid is isomorphic to the monoid of all nonconstant continuous selfmaps of a metrizable co-connected space. www.math.bas.bg /~serdica/n1_98.html

PlanetMath: derived category Call a morphism of chain complexes a quasi-isomorphism if it induces an isomorphism on homology groups of the For example, any chain homotopy is a quasi-isomorphism, but not conversely. Cross-references: derived functors, global sections, fixed, functors, algebra, place, localization, inverse, complexes, groups, homology, isomorphism, maps, classes, chain homotopy, morphisms, chain complexes, category, abelian category planetmath.org /encyclopedia/DerivedCategory.html

zuo_vie3.tex The second morphism in (\ref{3.1.3}) is an isomorphism on the largest open subset where $\tilde{\varphi}$ is an isomorphism, in particular on $\tilde{f}^{-1}(Y'_1)$. The morphism $\eta$ has reduced fibres over general points of divisors in $Y^\#$, hence it is smooth outside a codimension two subset of $Y'$, and replacing $Y$ by the complement of its image, we achieved c). Let us start with a finiteness result for morphisms from curves to $M_h$, close in spirit to the one obtained in \cite{B-V}, 4.3, in case that $M_h$ is the moduli space of surfaces of general type. www.uni-essen.de /~mat903/preprints/zuo_vie3.tex

hom11-19.txt Hi(Spec (k), G; Z=n) is an isomorphism, a result which would imply that (2) is a quasi-isomorphism and hence the Isomorphism Conjecture. Friedlander's isomorphism conjecture for G(C) and G(R) implies the equivariant isomorphism conjecture for G(C). Then we have natural (in G and A) isomorphisms Hi(Spec (k), G; A)~=Hi(G(k), A) Hi(Spec (k), G; A)~=Hi(G(k), A), for all i 0, where G(k) is the discrete group of k-rational points of G. Proof.This follows from the observation that C0(Gi= Spec(k)) is the free abelian group on k-points of Gi. hopf.math.purdue.edu /Knudson-Walker/hom11-19.txt

discreteccr.tex In particular, by the corollary of 3.2 we may conclude from these remarks that {\it there is a representation of the discretized $CCR$s $(2.2)$ which generates $R$ as a von Neumann algebra; moreover any finite representation of the discretized $CCR$s is quasi-equivalent to this one}. Since any two subfactors of $R$ of index 2 are known to be isomorphic \cite{12}, we have here a very stable invariant for the embedding of the discretized $CCR$ algebra in the irrational rotation algebra $\Cal A_\theta$. We show that when $\tau^2/\pi$ is irrational (e.g., when $\tau$ is a rational number), $C^*(P_\tau,Q_\tau)$ is isomorphic to the non-commutative sphere $\Cal B_{\tau^2}$ of Bratteli, Evans, Elliott and Kishimoto \cite{5}\cite{6}; hence it is a simple \cstar\ with a unique trace. math.berkeley.edu /~arveson/oldDvi/discreteccr.tex

Volume20 Volume 20 (1961) BRACE, JOHN W.: -Quasi uniform convergence versus almost uniform convergence. portmath.ptmat.fc.ul.pt /V/Volume20

Novi Sad Journal of Mathematics, Vol. 32, No. 2, pp. 131-140, 2002 Keywords: power algebra, good relation, quasi-congruence, isomorphism theorems In this paper we investigate some special classes of good relations for which the generalized versions of the well-known isomorphism theorems can be proved. Abstract: The notion of a good quotient relation has been introduced as an attempt to generalize the notion of a quotient algebra to relations on an algebra which are not necessarily congruence relations. www.mat.ub.es /EMIS/journals/NSJOM/32_2/14.html   (115 words)

Volume 154, No. 1, July 2001 H\"older continuity of the integrated density of states for quasi-periodic Schr\"odinger equations and averages of shifts of subharmonic functions. A counterexample to the isomorphism problem for integral group rings. Stable intersections of regular Cantor sets with large Hausdorff dimensins. www.math.princeton.edu /~annals/issues/2001/154_1_toc.html   (115 words)

Graduate Handbook First order quasi-linear equations and their application to physical and social sciences; the Cauchy-Kovalevsky theorem; characteristics, classification, and canonical form of linear equations; equations of mathematical physics; study of the Laplace, wave and heat equations; methods of solution. Group theory: definitions, examples, subgroups, quotient groups, homomorphisms, and isomorphism theorems. C*-algebras and representations, the noncommutative Gelfand-Naimark theorem, von Neumann algebras, and Murray-von Neumann equivalence. www.math.purdue.edu /academic/grad/handbook?id=9   (1800 words)

polynomialsystems76.txt The construction is based on the fact that (in the category of algebraic sets) a morphism which is bijective (one-to-one and onto) is not necessarily an isomorphism. Since V is a variety and g, a morphism of algebraic sets, it follows immediately from (1.7) that X, is a constructible set. In Part 7 we show that finitely many inputs (which can be chosen quite arbitrarily) are sufficient to separate those states of a system which are distinguishable. www.math.rutgers.edu /pub/sontag/polynomialsystems76.txt   (1800 words)

2.text This morphism is injective between complex manifolds of the same dimension and therefore an isomorphism on its image. For a preimage x 2 X of D we find a morphism of an open neighbourhood Um of x to Dm, such that the tuple restricted to Um is equivalent to the pull back of (Cm, Dm, ßm, ?m). V d,g,m is smooth at points D, where D is an integral curve of geometric genus g with the property that all the branches of each of its singularities are smooth. www.ubka.uni-karlsruhe.de /vvv/2003/mathematik/2/2.text   (1800 words)

hom11-19.txt A qfh-covering of X is an h-covering {pi} such that all the morphisms pi are quasi-finite. Hi(BG(k), Z=n) is an isomorphism in the following cases: (1) G finite, solvable, or the normalizer of a maximal torus in a reductive group; HOMOLOGY OF LINEAR GROUPS 11 (2) G = GLm in cohomological degrees i 3. Suppose Q is a finite group acting on a CW-complex X in such a way that if an element of Q fixes a cell of X, then it fixes it pointwise. hopf.math.purdue.edu /Knudson-Walker/hom11-19.txt   (1800 words)

masuoka.html In terms of extensions, I will give some method of constructing coquasi-bialgebras and classifying them up to coquasi-isomorphism. I am interested in classifying Hopf or bialgebras up to cocycle deformation rather than up to isomorphism. For this, it seems natural to extend the framework to coquasi-bialgebras, the dual notion of quasi bialgebras due to Drinfeld. info.fuw.edu.pl /~pmh/conf/pfiles/masuoka.html   (55 words)

Amazon.com: Books: Etale Cohomology. (PMS-33) To reinforce this connection even further, the author asks the reader to show that a morphism between two smooth varieties over a field is etale if and only if the morphism induces an isomorphism on the tangent spaces. A flat morphism is the algebraic analogue of a map whose fibers form a continuously varying family. The first chapter emphasizes the role of etale morphisms and their role in defining the etale topology. www.amazon.com /exec/obidos/tg/detail/-/0691082383?v=glance   (55 words)

Morita.txt Consider a commutati* *ve ring R and an invertible R-module Q. In other words, there exists another R-module * *Q0 and an isomorphism of R-modules Q R Q0~= R. Then tensor product with Q over R is a* * self- equivalence of the category of right R-modules (with quasi-inverse the tensor p* *roduct with Q0). Morita treats both contravariant equivalences (which* * he calls dualities of module categories) and covariant equivalences (which he calls isom* *orphisms of module categories) and shows that they always arise from suitable bimodules,* * either via contravariant hom functors (for `dualities') or via covariant hom functors * *and tensor products (for `isomorphisms'). A Quillen adjoint functor pair between stable model categories gives rise to* * total derived functors which are exact functors with respect to the triangulated structure; i* *n other words both total derived functors commute with suspension and preserve distinguished * *triangles. hopf.math.purdue.edu /Schwede/Morita.txt   (55 words)

Table of contents for Library of Congress control number 99087081 39 2 Torsion-Free Abelian Groups 47 2.1 Quasi-isomorphism and Isomorphism at p.......... 144 5.2 Isomorphism at p and Representation Type........ 135 4.3 Finite Rank Butler Groups and Isomorphism at p.. www.loc.gov /catdir/toc/99087081.html   (55 words)

commalg.org - the center for commutative algebra Quasi-isomorphic differential graded algebras give rise to 2-isomorphic differential graded schemes and a differential graded algebra can be recovered up to quasi-isomorphism from the differential graded scheme it defines. For instance, for algebraically closed fields, archimedean real closed fields, and vector spaces, we show that the isomorphism problem is \Pi^0_3 complete. Differential graded schemes can be glued with respect to an etale topology and fibered products of differential graded schemes correspond on the algebra level to derived tensor products. www.commalg.org /preprints/2002_12.shtml   (55 words)

chains.txt A better alternative is to have axioms to identify the singular cochain functor up to quasi-isomorphism in the category of E1 algebras. U between cochain theories induces a natural transformation of cohomology theories H*T! Since we are using the strong form of the Homotopy Axiom A.1 and the Product Axiom A.3, the natural transformation of cohomology theories is an isomorphism on every object X if and only if it is an isomorphism on coefficients. The singular cochain functor on spaces or, more generally, the normalized coc* *hain functor on simplicial sets gives a particular model for ordinary cohomology whe* *re all known additional structure is visible. hopf.math.purdue.edu /Mandell/chains.txt   (55 words)

2000e:16033 The incidence coalgebra $IP$ of $P$ is the graded free abelian group generated by isomorphism classes of posets in $P$ with grading induced by the rank of a poset and coproduct by $\Delta(p)=\sum\sb {x\in p}[\widehat{0},x]\otimes[x,\widehat{1}].$ An algebra structure on $IP$ is defined. Hopf algebras give a global algebraic framework for studying partially ordered sets; Ehrenborg defined, for each graded partially ordered set, a quasi-symmetric function, which induces a Hopf morphism from the Hopf algebra of graded posets to the Hopf algebra of quasi-symmetric functions. A graded poset $p$ is defined in the paper, along with a function $f\sb J(p)$ that has as output the maximal chains in $p$ with descent set contained in $J$. www.math.tamu.edu /~frank.sottile/summaries/2000e:16033.html   (55 words)

Novi Sad Journal of Mathematics, Vol. 32, No. 2, pp. 131-140, 2002 Keywords: power algebra, good relation, quasi-congruence, isomorphism theorems In this paper we investigate some special classes of good relations for which the generalized versions of the well-known isomorphism theorems can be proved. Abstract: The notion of a good quotient relation has been introduced as an attempt to generalize the notion of a quotient algebra to relations on an algebra which are not necessarily congruence relations. www.mat.ub.es /EMIS/journals/NSJOM/32_2/14.html   (115 words)

Cohomology_Fiber.txt By Bott-Samelson Theorem ([16] appendix 2 Theorem 1.4), it is _____ a quasi-isomorphism, since the functors H and T commute. Recall first that by the Bott-Samelson Theorem, the adjunction maps ad induce an isomorphism of graded coalgebras between T H+ (B) TH+(E) _ and H*(B) H*(E) _. Theorem 10.8 Let p be an odd prime and let f : E i B be a fibration of fiber F such that E and B are both (r; p)-mild with Hrp(f) injective. hopf.math.purdue.edu /Menichi/Cohomology_Fiber.txt   (11127 words)

masuoka.html In terms of extensions, I will give some method of constructing coquasi-bialgebras and classifying them up to coquasi-isomorphism. For this, it seems natural to extend the framework to coquasi-bialgebras, the dual notion of quasi bialgebras due to Drinfeld. I am interested in classifying Hopf or bialgebras up to cocycle deformation rather than up to isomorphism. www.fuw.edu.pl /~pmh/conf/pfiles/masuoka.html   (55 words)

Rational isomorphisms between K-theories and cohomology theories, by Eric M. Friedlander and Mark E. Walker Since semi-topological K-theory and morphic cohomology can be formulated as the semi-topological singular complexes associated to K-theory and motivic cohomology, this criterion provides a rational isomorphism between the semi-topological K-theory groups and the morphic cohomology groups of a smooth complex variety. The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the "Segre map") of infinite loop spaces. A technique is introduced which establishes a useful general criterion for a natural transformation of functors on quasi-projective complex varieties to induce a homotopy equivalence of semi-topological singular complexes. www.mathematik.uni-osnabrueck.de /K-theory/0557   (55 words)

h1104.txt The domain of the chain-level intersection pairing is a subcomplex G of C_*M\otimes C_*M. We prove that G is a ``full'' subcomplex, that is, the inclusion of G in C_*M \otimes C_*M is a quasi-isomorphism. Using this, we show that the intersection pairing gives C_*M a structure of partially defined commutative DGA, which in particular implies that C_*M is canonically quasi-isomorphic to an E_\infty chain algebra. An analogous result is true for the domain of the iterated intersection pairing. www.lehigh.edu /~dmd1/h1104.txt   (55 words)

CCSD thèses-EN-ligne: Homologies d'algèbres Artin-Schelter régulières cubiques La propriété de Koszul généralisée nous permet d'écrire un quasi-isomorphisme explicite entre le complexe qui calcule la cohomologie de Hochschild de $A$ et le complexe qui calcule l'homologie de Hochschild de $A$, obtenant ainsi une dualité de Poincaré. The Koszul property allows us to give an explicit quasi-isomorphism between the Hochschild cochain complex and the Hochschild chain complex. The de Rham cohomology, cyclic and periodic cyclic homologies are deduced from the Hochschild homology using standard results. tel.ccsd.cnrs.fr /documents/archives0/00/00/77/63/index_fr.html   (563 words)

Novi Sad Journal of Mathematics, Vol. 32, No. 2, pp. 131-140, 2002 Keywords: power algebra, good relation, quasi-congruence, isomorphism theorems In this paper we investigate some special classes of good relations for which the generalized versions of the well-known isomorphism theorems can be proved. Abstract: The notion of a good quotient relation has been introduced as an attempt to generalize the notion of a quotient algebra to relations on an algebra which are not necessarily congruence relations. www.mat.ub.es /EMIS/journals/NSJOM/32_2/14.html   (115 words)

commalg.org - the center for commutative algebra Quasi-isomorphic differential graded algebras give rise to 2-isomorphic differential graded schemes and a differential graded algebra can be recovered up to quasi-isomorphism from the differential graded scheme it defines. For a large class of singular varieties $Y$, we show that $\D_Y$-modules are equivalent to stratifications on $Y$ and thus in particular are unaffected by a class of homeomorphisms, the {\em cuspidal quotients}. These varieties can be interpreted as generalized tangent bundles over the classical determinantal varieties; a special case of these varieties first appeared in a problem in commuting matrices. www.commalg.org /preprints/2002_12.shtml   (2220 words)

Citebase - Cohomological construction of quantized universal enveloping algebras We prove that F can be chosen to satisfy some additional invariance conditions under (anti)automorphisms of U(\cG)[[h]], in particular, F gives an isomorphism of rigid quasi-tensor categories. A morphism of quasi-tensor structures is given by an element F∈ A (commutativity constraint), together with an antiautomorphism (antipode), S, of A satisfying the certain compatibility conditions. citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:q-alg/9506013   (424 words)

Chapter 3 - The Minkowski Question Mark and the Modular Group The representations are isomorphic, and the Minkowski Question Mark Function is shown to be the isomorphism. The Question Mark is defined only on the unit interval, or, at best, as a (quasi-)periodic function. From this we can deduce that the Minkowski Question Mark function is continuous and monotonically increasing, and that furthermore, it is defined on the reals. linas.org /math/chap-minkowski/chap-minkowski.html   (424 words)

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