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1.

図書
図書
1. Correspondences and duality
Dennis Gaitsgory, Nick Rozenblyum
出版情報: Providence, R.I. : American Mathematical Society, c2017  xl, 533 p. ; 27 cm
シリーズ名: Mathematical surveys and monographs ; v. 221 . A study in derived algebraic geometry ; v. 1
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2.

図書
図書
2. Deformations, Lie theory and formal geometry
Dennis Gaitsgory, Nick Rozenblyum
出版情報: Providence, R.I. : American Mathematical Society, c2017  xxxv, 436 p. ; 27 cm
シリーズ名: Mathematical surveys and monographs ; v. 221 . A study in derived algebraic geometry ; v. 2
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3.

図書
図書
3. Abstract algebra : applications to Galois theory, algebraic geometry, representation theory and cryptography. 2nd ed
Celine Carstensen-Opitz ... [et al.]
出版情報: Berlin : De Gruyter, c2019  xiii, 407 p. ; 24 cm
シリーズ名: De Gruyter graduate
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目次情報: 続きを見る
Preface
Preface to the second edition
Groups, rings and fields / 1：
Abstract algebra / 1.1：
Rings / 1.2：
Integral domains and fields / 1.3：
Subrings and ideals / 1.4：
Factor rings and ring homomorphisms / 1.5：
Fields of fractions / 1.6：
Characteristic and prime rings / 1.7：
Groups / 1.8：
Exercises / 1.9：
Maximal and prime ideals / 2：
Prime ideals and integral domains / 2.1：
Maximal ideals and fields / 2.3：
The existence of maximal ideals / 2.4：
Principal ideals and principal ideal domains / 2.5：
Prime elements and unique factorization domains / 2.6：
The fundamental theorem of arithmetic / 3.1：
Prime elements, units and irreducibles / 3.2：
Unique factorization domains / 3.3：
Principal ideal domains and unique factorization / 3.4：
Euclidean domains / 3.5：
Overview of integral domains / 3.6：
Polynomials and polynomial rings / 3.7：
Polynomial rings over fields / 4.1：
Polynomial rings over integral domains / 4.3：
Polynomial rings over unique factorization domains / 4.4：
Field extensions / 4.5：
Extension fields and finite extensions / 5.1：
Finite and algebraic extensions / 5.2：
Minimal polynomials and simple extensions / 5.3：
Algebraic closures / 5.4：
Algebraic and transcendental numbers / 5.5：
Field extensions and compass and straightedge constructions / 5.6：
Geometric constructions / 6.1：
Constructible numbers and field extensions / 6.2：
Four classical construction problems / 6.3：
Squaring the circle / 6.3.1：
The doubling of the cube / 6.3.2：
The trisection of an angle / 6.3.3：
Construction of a regular n-gon / 6.3.4：
Kronecker's theorem and algebraic closures / 6.4：
Kronecker's theorem / 7.1：
Algebraic closures and algebraically closed fields / 7.2：
The fundamental theorem of algebra / 7.3：
Splitting fields / 7.3.1：
Permutations and symmetric polynomials / 7.3.2：
The fundamental theorem of symmetric polynomials / 7.4：
Skew field extensions of C and Frobenius's theorem / 7.6：
Splitting fields and normal extensions / 7.7：
Normal extensions / 8.1：
Groups, subgroups, and examples / 8.3：
Groups, subgroups, and Isomorphisms / 9.1：
Examples of groups / 9.2：
Permutation groups / 9.3：
Cosets and Lagrange's theorem / 9.4：
Generators and cyclic groups / 9.5：
Normal subgroups, factor groups, and direct products / 9.6：
Normal subgroups and factor groups / 10.1：
The group isomorphism theorems / 10.2：
Direct products of groups / 10.3：
Finite Abelian groups / 10.4：
Some properties of finite groups / 10.5：
Automorphisms of a group / 10.6：
Symmetric and alternating groups / 10.7：
Symmetric groups and cycle decomposition / 11.1：
Parity and the alternating groups / 11.2：
Conjugation in Sn / 11.3：
The simplicity of An / 11.4：
Solvable groups / 11.5：
Solvability and solvable groups / 12.1：
The derived series / 12.2：
Composition series and the Jordan-Holder theorem / 12.4：
Groups actions and the Sylow theorems / 12.5：
Group actions / 13.1：
Conjugacy classes and the class equation / 13.2：
The Sylow theorems / 13.3：
Some applications of the Sylowtheorems / 13.4：
Free groups and group presentations / 13.5：
Group presentations and combinatorial group theory / 14.1：
Free groups / 14.2：
Group presentations / 14.3：
The modular group / 14.3.1：
Presentations of subgroups / 14.4：
Geometric interpretation / 14.5：
Presentations of factor groups / 14.6：
Group presentations and decision problems / 14.7：
Group amalgams: free products and direct products / 14.8：
Finite Galois extensions / 14.9：
Galois theory and the solvability of polynomial equations / 15.1：
Automorphism groups of field extensions / 15.2：
The fundamental theorem of Galois theory / 15.3：
Separable field extensions / 15.5：
Separability of fields and polynomials / 16.1：
Perfect fields / 16.2：
Finite fields / 16.3：
Separable extensions / 16.4：
Separability and Galois extensions / 16.5：
The primitive element theorem / 16.6：
Applications of Galois theory / 16.7：
Field extensions by radicals / 17.1：
Cyclotomic extensions / 17.3：
Solvability and Galois extensions / 17.4：
The insolvability of the quintic polynomial / 17.5：
Constructibility of regular n-gons / 17.6：
The theory of modules / 17.7：
Modules over rings / 18.1：
Annihilators and torsion / 18.2：
Direct products and direct sums of modules / 18.3：
Free modules / 18.4：
Modules over principal ideal domains / 18.5：
The fundamental theorem for finitely generated modules / 18.6：
Finitely generated Abelian groups / 18.7：
The fundamental theorem: p-primary components / 19.1：
The fundamental theorem: elementary divisors / 19.3：
Integral and transcendental extensions / 19.4：
The ring of algebraic integers / 20.1：
Integral ring extensions / 20.2：
Transcendental field extensions / 20.3：
The transcendence of e and ¿ / 20.4：
The Hilbert basis theorem and the nullstellensatz / 20.5：
Algebraic geometry / 21.1：
Algebraic varieties and radicals / 21.2：
The Hilbert basis theorem / 21.3：
The Hilbert nullstellensatz / 21.4：
Applications and consequences of Hilbert's theorems / 21.5：
Dimensions / 21.6：
Algebras and group representations / 21.7：
Group representations / 22.1：
Representations and modules / 22.2：
Semisimple algebras and Wedderburn's theorem / 22.3：
Ordinary representations, characters and character theory / 22.4：
Burnside's theorem / 22.5：
Algebraic cryptography / 22.6：
Basic cryptography / 23.1：
Encryption and number theory / 23.2：
Public key cryptography / 23.3：
The Diffie-Hellman protocol / 23.3.1：
The RSA algorithm / 23.3.2：
The El-Gamal protocol / 23.3.3：
Elliptic curves and elliptic curve methods / 23.3.4：
Noncommutative-group-based cryptography / 23.4：
Free group cryptosystems / 23.4.1：
Ko-Lee and Anshel-Anshel-Goldfeld methods / 23.5：
The Ko-Lee protocol / 23.5.1：
The Anshel-Anshel-Goldfeld protocol / 23.5.2：
Platform groups and braid group cryptography / 23.6：
Bibliography / 23.7：
Index
Preface
Preface to the second edition
Groups, rings and fields / 1：
4.

図書
図書
4. Global calculus
S. Ramanan
出版情報: Providence, R.I. : American Mathematical Society, c2005  xi, 316 p. ; 27 cm
シリーズ名: Graduate studies in mathematics ; v. 65
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Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1：
Sheaves and Presheaves / 1：
Basic Constructions / 2：
Differential Manifolds / 3：
Lie Groups; Action on a Manifold / 4：
Exercises
Differential Operators / Chapter 2：
First Order Differential Operators
Locally Free Sheaves and Vector Bundles
Flow of a Vector Field
Theorem of Frobenius
Tensor Fields; Lie Derivative / 5：
The Exterior Derivative; de Rham Complex / 6：
Differential Operators of Higher Order / 7：
Integration on Differential Manifolds / Chapter 3：
Integration on a Manifold
Sheaf of Densities
Adjoints of Differential Operators
Cohomology of Sheaves and Applications / Chapter 4：
Injective Sheaves
Sheaf Cohomology
Cohomology through Other Resolutions
Singular and Sheaf Cohomologies
Cech and Sheaf Cohomologies
Differentiable Simplices; de Rham's Theorem
Connections on Principal and Vector Bundles; Lifting of Symbols / Chapter 5：
Connections in a Vector Bundle
The Space of All Connections on a Bundle
Principal Bundles
Connections on Principal Bundles
Curvature
Chern-Weil Theory
Holonomy Group; Ambrose-Singer Theorem
Linear Connections / Chapter 6：
Lifting of Symbols and Torsion
Manifolds with Additional Structures / Chapter 7：
Reduction of the Structure Group
Torsion Free G-Connections
Complex Manifolds
The Outer Gauge Group
Riemannian Geometry
Riemannian Curvature Tensor
Ricci, Scalar and Weyl Curvature Tensors
Clifford Structures and the Dirac Operator / 8：
Local Analysis of Elliptic Operators / Chapter 8：
Regularisation
A Characterisation of Densities
Schwartz Space of Functions and Densities
Fourier Transforms
Distributions
Theorem of Sobolev
Interior Regularity of Elliptic Solutions
Vanishing Theorems and Applications / Chapter 9：
Elliptic Operators on Differential Manifolds
Elliptic Complexes
Composition Formula
A Vanishing Theorem
Hodge Decomposition
Lefschetz Decomposition
Kodaira's Vanishing Theorem
The Imbedding Theorem
Appendix
Algebra
Topology
Analysis
Bibliography
Index
Preface
Sheaves and Differential Manifolds: Definitions and Examples / Chapter 1：
Sheaves and Presheaves / 1：
5.

図書
図書
5. Classical groups and geometric algebra
Larry C. Grove
出版情報: Providence, R.I. : American Mathematical Society, c2002  x, 169 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 39
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6.

図書
図書
6. Mehrdimensionale Projektive und Höhere Geometrie
von Werner Burau
出版情報: Berlin : Deutscher Verlag der Wissenschaften, 1961  436 p. ; 25 cm
シリーズ名: Mathematische Monographien ; 5
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7.

図書
図書
7. Introduction to Grothendieck duality theory
[by] Allen Altman [and] Steven Kleiman
出版情報: Berlin : Springer-Verlag, 1970  184 p. ; 26 cm
シリーズ名: Lecture notes in mathematics ; 146
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8.

図書
図書
8. Basic algebraic geometry (: gw ; : us)
I.R. Shafarevich ; translated from the Russian by K.A. Hirsch
出版情報: Berlin ; New York : Springer-Verlag, 1974  xv, 439 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 213
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9.

図書
図書
9. Topics in transcendental algebraic geometry (: pbk)
edited by Phillip Griffiths
出版情報: Princeton, N.J. : Princeton University Press, 1984  viii, 316 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 106
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10.

図書
図書
10. Selected topics in algebra and its interrelations with logic, number theory, and algebraic geometry
Ionel Bucur ; translated from the Romanian by Mihnea Moroianu
出版情報: București, Romania : Editura Academiei , Dordrecht ; Boston : D. Reidel , Hingham, MA, U.S.A. : Distributors for the U.S.A. and Canada, Kluwer Academic Publishers, c1984  viii, 406 p. ; 23 cm
シリーズ名: Mathematics and its applications ; East European series
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