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1.

図書
図書
1. An invitation to quantum cohomology : Kontsevich's formula for rational plane curves
Joachim Kock, Israel Vainsencher
出版情報: Boston : Birkhäuser, c2007  xii, 159 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 249
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Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：
Cross ratios / 0.1：
Definition of moduli space / 0.2：
Stable n-pointed Curves / 1：
n-pointed smooth rational curves / 1.1：
Stable n-pointed rational curves / 1.2：
Stabilization, forgetting marks, contraction / 1.3：
Sketch of the construction of [Characters not reproducible subscript 0,n] / 1.4：
The boundary / 1.5：
Generalizations and references / 1.6：
Stable Maps / 2：
Maps P[superscript 1 Characters not reproducible] P[superscript r] / 2.1：
1-parameter families / 2.2：
Kontsevich stable maps / 2.3：
Idea of the construction of [Characters not reproducible subscript 0,n] (P[superscript r], d) / 2.4：
Evaluation maps / 2.5：
Forgetful maps / 2.6：
Easy properties and examples / 2.7：
Complete conics / 2.9：
Enumerative Geometry via Stable Maps / 2.10：
Classical enumerative geometry / 3.1：
Counting conics and rational cubics via stable maps / 3.2：
Kontsevich's formula / 3.3：
Transversality and enumerative significance / 3.4：
Stable maps versus rational curves / 3.5：
Gromov-Witten Invariants / 3.6：
Definition and enumerative interpretation / 4.1：
Properties of Gromov-Witten invariants / 4.2：
Recursion / 4.3：
The reconstruction theorem / 4.4：
Quantum Cohomology / 4.5：
Quick primer on generating functions / 5.1：
The Gromov-Witten potential and the quantum product / 5.2：
Associativity / 5.3：
Kontsevich's formula via quantum cohomology / 5.4：
Bibliography / 5.5：
Index
Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：
2.

図書
図書
2. Notes on crystalline cohomology (: [pbk.] ; : hardcover)
by Pierre Berthelot, Arthur Ogus
出版情報: Princeton, N.J. : Princeton University Press, [20--]  1 v. ; 24 cm
シリーズ名: Princeton legacy library
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3.

図書
図書
3. Computational homology (: softcover)
Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
出版情報: New York ; Tokyo : Springer, c2004  xvii, 480 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 157
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4.

図書
図書
4. Gröbner bases and the computation of group cohomology
David J. Green
出版情報: Berlin ; Tokyo : Springer-Verlag, c2003  xi, 138 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1828
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5.

図書
図書
5. Cohomology rings of finite groups : with an appendix: calculations of cohomology rings of groups of order dividing 64
by Jon F. Carlson ... [et al.]
出版情報: Dordrecht : Kluwer Academic, c2003  xv, 776 p. ; 25 cm
シリーズ名: Algebras and applications ; v. 3
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Preface
Acknowledgements
Homological Algebra / 1：
Introduction
Complexes and Sequences / 2：
Projective and Injective Models / 3：
Resolutions / 4：
Ext / 5：
Tensor Products and Tor / 6：
Group Algebras
Duality and Tensor Products
Induction and Restriction
Radicals, Socles and Projective Modules
Degree Shifting
The Stable Category
Group Cohomology and Change of Coefficients / 7：
Projective Resolutions
Minimal Resolutions
The Bar Resolution
Applications to Low Dimensional Cohomology
Restrictions, Inflations and Transfers
Cohomology Products
Yoneda Splices and Compositions of Chain Maps
Products and Group Algebras
Restriction, Inflation and Transfer
Cohomology Ring Computations
Shifted Subgroups and Restrictions
Automorphisms and Cohomology
Spectral Sequences
The Spectral Sequence of a Biocomplex
Products
The Lyndon-Hochschild-Serre Spectral Sequence
Extension Classes
Minimal Resolutions and Convergence
Exact Couples and the Bockstein Spectral Sequence
Norms and the Cohomology of Wreath Products
Wreath Products
The Norm Map
Examples and Applications
Finite Generation of Cohomology
Steenrod Operations
The Steenrod Algebra and Modules
The Steenrod Operations on Cohomology
Cohomology and Modules Over the Steenrod Algebra
The Cohomology of Extraspecial 2-Groups
The Cohomology of Extraspecial p-Groups
Serre's Theorem on the Vanishing of Bocksteins
Varieties and Elementary Abelian Subgroups / 8：
Filtrations on Modules
Vanishing Products of Cohomology Elements
Minimal Primes in Cohomology Rings
The Stratification Theorem
Cohomology Rings of Modules / 9：
Generalized Bocksteins Over Elementary Abelian Groups
Rank Varieties and Cohomology Rings Over Elementary Abelian Groups
The Cohomological Support Variety of a Module
Equating the Rank and Cohomological Support Varieties
The Tensor Product Theorem
Properties of the Cohomological Support Varieties
Complexity and Multiple Complexes / 10：
Notes on Dimension and Rates of Growth
Complexity of Modules
Varieties for Modules with Other Coefficient Rings
Projective Resolutions as Multiple Complexes
Duality Complexes / 11：
Gaps in Cohomology
PoincarF Duality Complexes
Differentials in the HSS
Cohen Macaulay Cohomology Rings
Further Considerations
Transfers, Depth and Detection / 12：
Notes on Depth and Associated Primes
Depth and the p-Rank of the Center
Varieties and Transfers
Detection and Depth-Essential Cohomology
Special Cases
Associated Primes in Cohomology
Unstable Modules
Subgroup Complexes / 13：
Posets of Subgroups and Cell Complexes
Homotopy Equivalences and Equivariance
Complexes of Posets of Finite Groups
The Bouc Complex
Applications to Cohomology
Decompositions of Molecules
Additional Remarks
Cohomology Compositions
Computer Calculations and Completion Tests / 14：
The Visual Cohomology Ring: Generators and Relations
Resolutions, Maps and Homogeneous Parameters
Tests for Completion
Two Special Cases
Appendices: Calculations of the Cohomology Rings of Groups of Order Dividing 64 / J.F. Carlson ; L. Valero-Elizondo ; Mucheng Zhang
Notation and References / A：
Groups of Order 8 / B：
Groups of Order 16 / C：
Groups of Order 32 / D：
Groups of Order 64 / E：
Tables of Krull Dimension and Depth / F：
Tables of Hilbert/PoincarF Series / G：
References
Index
Preface
Acknowledgements
Homological Algebra / 1：
6.

図書
図書
6. Secondary cohomology operations (: hbk ; : pbk)
John R. Harper
出版情報: Providence, R.I. : American Mathematical Society, c2002  xi, 268 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 49
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Review of primary operations
Segue to secondary operations
Fundamental constructions
Secondary cohomology operations
Calculations with secondary operations
The Hopf invariant
The cohomology structure of universal examples
Bibliography
Index
Review of primary operations
Segue to secondary operations
Fundamental constructions
7.

図書
図書
7. Weil conjectures, perverse sheaves and l'adic Fourier transform
Reinhardt Kiehl, Rainer Weissauer
出版情報: Berlin ; Heiderlberg : Springer, c2001  xii, 375 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 42 . A series of modern surveys in mathematics
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8.

図書
図書
8. Homology of linear groups (: sz ; : us)
Kevin P. Knudson
出版情報: Basel ; Boston : Birkhäuser Verlag, c2001  xi, 192 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 193
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9.

図書
図書
9. Rigid cohomology (: hbk)
Bernard Le Stum
出版情報: Cambridge : Cambridge University Press, 2007  xv, 319 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 172
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Preface
Introduction / 1：
Alice and Bob / 1.1：
Complexity / 1.2：
Weil conjectures / 1.3：
Zeta functions / 1.4：
Arithmetic cohomology / 1.5：
Bloch-Ogus cohomology / 1.6：
Frobenius on rigid cohomology / 1.7：
Slopes of Frobenius / 1.8：
The coefficients question / 1.9：
F-isocrystals / 1.10：
Tubes / 2：
Some rigid geometry / 2.1：
Tubes of radius one / 2.2：
Tubes of smaller radius / 2.3：
Strict neighborhoods / 3：
Frames / 3.1：
Frames and tubes / 3.2：
Strict neighborhoods and tubes / 3.3：
Standard neighborhoods / 3.4：
Calculus / 4：
Calculus in rigid analytic geometry / 4.1：
Examples / 4.2：
Calculus on strict neighborhoods / 4.3：
Radius of convergence / 4.4：
Overconvergent sheaves / 5：
Overconvergent sections / 5.1：
Overconvergence and abelian sheaves / 5.2：
Dagger modules / 5.3：
Coherent dagger modules / 5.4：
Overconvergent calculus / 6：
Stratifications and overconvergence / 6.1：
Cohomology / 6.2：
Cohomology with support in a closed subset / 6.3：
Cohomology with compact support / 6.4：
Comparison theorems / 6.5：
Overconvergent isocrystals / 7：
Overconvergent isocrystals on a frame / 7.1：
Overconvergence and calculus / 7.2：
Virtual frames / 7.3：
Cohomology of virtual frames / 7.4：
Rigid cohomology / 8：
Overconvergent isocrystal on an algebraic variety / 8.1：
Frobenius action / 8.2：
Conclusion / 9：
A brief history / 9.1：
Crystalline cohomology / 9.2：
Alterations and applications / 9.3：
The Crew conjecture / 9.4：
Kedlaya's methods / 9.5：
Arithmetic D-modules / 9.6：
Log poles / 9.7：
References
Index
Preface
Introduction / 1：
Alice and Bob / 1.1：
10.

図書
図書
10. Symmetric functions, Schubert polynomials and degeneracy loci
Laurent Manivel ; translated by John R. Swallow
出版情報: Providence, R.I. : American Mathematical Society , [Paris] : Société Mathématique de France, c2001  vii, 167 p. ; 26 cm
シリーズ名: SMF/AMS texts and monographs ; v. 6
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Introduction
The ring of symmetric functions
Schubert polynomials
Schubert varieties A brief Introduction to singular homology
Bibliography
Index
Introduction
The ring of symmetric functions
Schubert polynomials
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