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Books on the topic 'Torsion theory (algebra)'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 March 2023

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1

Bland, Paul E. Topics in torsion theory. Berlin, F.R.G: Wiley-VCH, 1998.

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2

Torsion theories. Harlow, Essex, England: Longman Scientific & Technical, 1986.

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3

Call, Frederick W. Torsion theoretic algebraic geometry. Kingston, Ont. Canada: Queen's University, 1989.

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4

Brandal, Willy. Torsion theories over commutative rings. Moscow, Idaho: BCS Associates, 1996.

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5

Sebastian, Goette, ed. Families torsion and Morse functions. Paris: Société mathématique de France, 2001.

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6

Gardner, B. J. Radical theory. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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7

Calegari, Frank. A torsion Jacquet-Langlands correspondence. Paris: Société Mathématique de France, 2019.

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8

Fujita, Yasutsugu. Torsion of elliptic curves over number fields. Sendai, Japan: Tohoku University, 2003.

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9

Beligiannis, Apostolos. Homological and homotopical aspects of Torsion theories. Providence, RI: American Mathematical Society, 2007.

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10

Teply, Mark L. Semicocritical modules. [Murcia (España)]: Secretariado de Publicaciones e Intercambio Científico, Universidad de Murcia (España), 1986.

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11

Luis, Oyonarte, ed. Covers, envelopes, and cotorsion theories. New York: Nova Science, 2002.

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12

Harold, Simmons, ed. Derivatives, nuclei, and dimensions on the frame of torsion theories. Harlow, Essex, England: Longman Scientific & Technical, 1988.

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13

Torsions of 3-dimensional manifolds. Boston: Birkhauser Verlag, 2002.

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14

Linear topologies on a ring: An overview. Harlow, Essex, England: Longman Scientific & Technical, 1987.

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15

Linear topologies on a ring: An overview. Harlow: Longman Scientific & Technical, 1987.

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16

B, Carrell James, and McGovern William M. 1959-, eds. Algebraic quotients: Torus actions and cohomology / J.B. Carrell. The adjoint representation and the adjoint action / W.M. McGovern. Berlin: Springer, 2002.

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17

Adelmann, Clemens. Decomposition of Primes in Torsion Point Fields. Springer London, Limited, 2004.

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18

Derivatives, Nuclei and Dimensions on the Frame of Torsion Theories. Pearson Education, Limited, 1988.

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19

The Decomposition of Primes in Torsion Point Fields. Springer, 2001.

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20

Introduction to Combinatorial Torsions. Birkhäuser Basel, 2001.

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21

Homological and Homotopical Aspects of Torsion Theories (Memoirs of the American Mathematical Society). Amer Mathematical Society, 2007.

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22

Lopez, Jose E. Navas. Multiplication Objects in Monoidal Categories. Nova Science Publishers, 2000.

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23

Torsors Tale Homotopy And Applications To Rational Points. Cambridge University Press, 2013.

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24

Bialynicki-Birula, A., J. Carrell, and W. M. McGovern. Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action. Springer, 2002.

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25

Organized Collapse: An Introduction to Discrete Morse Theory. American Mathematical Society, 2021.

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26

Organized Collapse: An Introduction to Discrete Morse Theory. American Mathematical Society, 2020.

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27

Radical Theory (Pitman Research Notes in Mathematics). Longman Higher Education Division (a Pearson Education company), 1989.

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28

Farb, Benson, and Dan Margalit. The Symplectic Representation and the Torelli Group. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0007.

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This chapter discusses the basic properties and applications of a symplectic representation, denoted by Ψ‎, and its kernel, called the Torelli group. After describing the algebraic intersection number as a symplectic form, the chapter presents three different proofs of the surjectivity of Ψ‎, each illustrating a different theme. It also illustrates the usefulness of the symplectic representation by two applications to understanding the algebraic structure of Mod(S). First, the chapter explains how this representation is used by Serre to prove the theorem that Mod(Sɡ) has a torsion-free subgroup of finite index. It thens uses the symplectic representation to prove, following Ivanov, the following theorem of Grossman: Mod(Sɡ) is residually finite. It also considers some of the pioneering work of Dennis Johnson on the Torelli group. In particular, a Johnson homomorphism is constructed and some of its applications are given.

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29

Abbes, Ahmed, and Michel Gros. Representations of the fundamental group and the torsor of deformations. Local study. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691170282.003.0002.

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This chapter focuses on representations of the fundamental group and the torsor of deformations. It considers the case of an affine scheme of a particular type, qualified also as small by Faltings. It introduces the notion of Dolbeault generalized representation and the companion notion of solvable Higgs module, and then constructs a natural equivalence between these two categories. It proves that this approach generalizes simultaneously Faltings' construction for small generalized representations and Hyodo's theory of p-adic variations of Hodge–Tate structures. The discussion covers the relevant notation and conventions, results on continuous cohomology of profinite groups, objects with group actions, logarithmic geometry lexicon, Faltings' almost purity theorem, Faltings extension, Galois cohomology, Fontaine p-adic infinitesimal thickenings, Higgs–Tate torsors and algebras, Dolbeault representations, and small representations. The chapter also describes the descent of small representations and applications and concludes with an analysis of Hodge–Tate representations.

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30

Abbes, Ahmed, and Michel Gros. Representations of the fundamental group and the torsor of deformations. Global aspects. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691170282.003.0003.

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This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

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31

Abbes, Ahmed, and Michel Gros. Representations of the fundamental group and the torsor of deformations. An overview. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691170282.003.0001.

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This chapter provides an overview of a new approach to the p-adic Simpson correspondence, focusing on representations of the fundamental group and the torsor of deformations. The discussion covers the notation and conventions, small generalized representations, the torsor of deformations, Faltings ringed topos, and Dolbeault modules. The chapter begins with a short aside on small generalized representations in the affine case, which will be used as intermediary for the study of Dolbeault representations. It then introduces the notion of generalized Dolbeault representation for a small affine scheme and the companion notion of solvable Higgs module, and constructs a natural equivalence between these two categories. It establishes links between these notions and Faltings smallness conditions and relates this to Hyodo's theory. It also describes the Higgs–Tate algebras and concludes with an analysis of the logical links for a Higgs bundle, between smallness and solvability.

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32

Abbes, Ahmed, Michel Gros, and Takeshi Tsuji. The p-adic Simpson Correspondence (AM-193). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691170282.001.0001.

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The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches. It mainly focuses on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The book shows the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the book contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored.

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