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Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-02T14:09:22Z No. of bitstreams: 1 Arquivototal.pdf: 978771 bytes, checksum: bf0c05c8da5e986a77b6215a2235ab5e (MD5) / Made available in DSpace on 2018-05-02T14:09:22Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 978771 bytes, checksum: bf0c05c8da5e986a77b6215a2235ab5e (MD5) Previous issue date: 2017-04-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / At the end of the 60s, Andr e and Quillen introduced a cohomology theory for commutative algebras, which today is called Andr e-Quillen's cohomology. In this work, we will study K ahler di erential functor, which is here seen as a derived functor (in a nonabelian context), which connects the categories: simpli ed R-algebras and simpli ed R-modules. In the rst, through simplicial resolutions, we will notice that they characterize certain objects and diagrams of this model category, which in turn, are preserved by K ahler di erential functor. In addition, we will approach the complex cotangent of a R-algebra, and through it, de ne the homology and cohomology of Andr e-Quilen, and of course, expose some properties of these. / No nal da década de 60, André e Quillen introduziram uma teoria de cohomologia para álgebras comutativas, que hoje recebe o nome de cohomologia de André-Quillen. Neste trabalho, estudaremos o funtor de diferenciais de K ahler, que aqui é visto como funtor derivado (em um contexto não abeliano), que conecta as categorias: R-álgebras simpliciais e R-m odulos simpliciais. Na primeira, atrav es das resolu c~oes simpliciais, notaremos que estas caracterizam certos objetos e diagramas desta categoria modelo, que por sua vez, s~ao preservados pelo funtor de diferenciais de K ahler. Al em disso, abordaremos o complexo cotangente de uma R- algebra, e atrav es dele, de nir a homologia e cohomologia de André-Quillen, e naturalmente, expor algumas propriedades destas.

A motivational problem for group homology is a conjecture of Quillen that states, as reformulated by Anton, that the second homology of the general linear group over R = Z[1/p; ζp], for p an odd prime, is isomorphic to the second homology of the group of units of R, where the homology calculations are over the field of order p. By considering the group extension spectral sequence applied to the short exact sequence 1 → SL2 → GL2 → GL1 → 1 we show that the calculation of the homology of SL2 gives information about this conjecture. We also present a series of algorithms that finds an upper bound on the second homology group of a finitely-presented group. In particular, given a finitely-presented group G, Hopf's formula expresses the second integral homology of G in terms of generators and relators; the algorithms exploit Hopf's formula to estimate H2(G; k), with coefficients in a finite field k. We conclude with sample calculations using the algorithms.

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United States Public Law 92-541, commonly known as the Teague-Cranston Act, called for the creation of five new medical schools in five states to meet the needs of medically under served areas of the country. The act, as passed, required that the new schools be "located in proximity to, and operated in conjunction with, Veterans' Administration medical facilities." This worked in ETSU's favor as the university is located adjacent to the Mountain Home VA Hospital. Signed into law by President Richard Nixon, this would eventually lead to the establishment of the Quillen College of Medicine.

Following the passage of the Teague-Cranston Act, on February 14, 1974 Senator Nave of the Tennessee General Assembly called for consideration of state legislation to establish a medical school at East Tennessee State University. Eventually passing both the Tennessee House and Senate, the bill was vetoed by Governor Winfield Dunn of Memphis. Motions to override the veto were made in both chambers and were successful. Senate Bill no.1549 became law on March 6, 1974.

With the passage of the Teague-Cranston Act and efforts to establish a medical school underway in the Tennessee Legislature, East Tennessee State University had already begun the planning process for the new medical school. This plan was submitted to the Tennessee Board of Regents on February 1, 1974 by the ETSU Medical Education Study Committee which clarified the specifics of what the Quillen College of Medicine would eventually become. The physical copy of this item can be found in the Archives of Appalachia at East Tennessee State University. For access or more information please contact the Archives of Appalachia.

Following the passage of the Teague-Cranston Act and Tennessee state legislation, with the Plan for Medical Education in place, the next step was qualifying for federal funds. With the help of U.S. Representative Jimmy Quillen and the State Board of Regents Chancellor Roy Nicks, the application for funds was approved by the Veterans Administration on July 11, 1974. However, it was not until Dr. Culp's last day in office as President of ETSU, that the Liason Committee on Medical Education issued a letter of reasonable assurance that the new medical school would be accredited. The physical copy of this item can be found in the Archives of Appalachia at East Tennessee State University. For access to the physical copy or more information please contact the Archives of Appalachia.

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This thesis summarises the author's results in representation theory of rings and schemes, obtained with several collaborators. First, we show that for a quasicompact semiseparated scheme X, the derived category of very flat quasicoherent sheaves is equivalent to the derived category of flat quasicoherent sheaves, and if X is affine, this is further equivalent to the homotopy category of projectives. Next, we prove that if R is a commutative Noetherian ring, then every countably generated flat module is quite flat, i.e., a direct summand of a transfinite extension of localizations of R in countable multiplicative subsets. Further, we investigate the relations between the geometric and categorical purity in categories of sheaves; we give a characterization of indecomposable geometric pure-injectives in both the quasicoherent and non-quasicoherent case. In partic- ular, we describe the Ziegler spectrum and its geometric part for the category of quasicoherent sheaves on the projective line over a field. The final result is the equivalence of the following statements for a quasicompact quasiseparated scheme X: (1) the category QCoh(X) of all quasicoherent sheaves on X has a flat generator; (2) for every injective object E of QCoh(X), the internal Hom functor into E is exact; (3) for some injective...