Kuga Varieties(久賀簇) : Fiber Varieties over a Symmetric Space Whose Fibers Are Abeliean Varieties 9787040503043, 7040503042
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English Pages 175 Year 2018
Table of contents :
Acknowledgements
Contents
Volume l
Chapter I. Vector bundle valued harmonic forms
1. An analogy of de Rham's theorem
2. Harmonic ρ-forms
3. The type decomposition of harmonie ρ-forms
4. Mountjoy's abelian varieties
5. Commutativity with ⊿_A (A weak analogue of a theorem of Chern, by A. Weil, Matsushima, Murakami, and others)
6. Proof of commutativity theorems
7. A wider frame: spherical functions
8. An example: G = SL(2, R)
9. Other examples, and discussions
Chapter II. Fibre variety over a symmetric space whose fibres are abelian varieties
1. A fibre bundle V xrightarrow{; pi ;} U
2. Cohomology groups of V (Part I)
3. Cohomology groups of V (Part II)
4. Up-side-down operator θ, and the θ-invariant subspaces of H_2(V)
5. Fibre variety over a symmetric space whose fibres are abelian varieties
6. Algebraic family of polarized abelian varieties
7. Minimality of quotient varieties
Appendix I. A letter of André Weil
Appendix II. Holomorphic imbeddings of symmetric domains into a Siegel space
References for volume I: 1-17
18-43
44-69
70-95
Volume II
Chapter III. Hecke operators
1. Goldman adelilzation
2. Hecke operator operating on H^P (X, Γ, ρ) etc.
3. Hecke operator operating on Ω(X × F)
4. Hecke operators as algebraic correspondences
Chapter IV. Number theory of automorphic forms
1. A fibre variety over an algebraic curve U = Γ X
2. Harmonie forms on V, and the trace formulas
3. Zeta-function of widetilde{V}^p
4. Congruence Artin - L-functions
5. Hecke polynomials as L-functions
References for volume II: 1-17
18-43
44-69
70-95
Acknowledgements
Contents
Volume l
Chapter I. Vector bundle valued harmonic forms
1. An analogy of de Rham's theorem
2. Harmonic ρ-forms
3. The type decomposition of harmonie ρ-forms
4. Mountjoy's abelian varieties
5. Commutativity with ⊿_A (A weak analogue of a theorem of Chern, by A. Weil, Matsushima, Murakami, and others)
6. Proof of commutativity theorems
7. A wider frame: spherical functions
8. An example: G = SL(2, R)
9. Other examples, and discussions
Chapter II. Fibre variety over a symmetric space whose fibres are abelian varieties
1. A fibre bundle V xrightarrow{; pi ;} U
2. Cohomology groups of V (Part I)
3. Cohomology groups of V (Part II)
4. Up-side-down operator θ, and the θ-invariant subspaces of H_2(V)
5. Fibre variety over a symmetric space whose fibres are abelian varieties
6. Algebraic family of polarized abelian varieties
7. Minimality of quotient varieties
Appendix I. A letter of André Weil
Appendix II. Holomorphic imbeddings of symmetric domains into a Siegel space
References for volume I: 1-17
18-43
44-69
70-95
Volume II
Chapter III. Hecke operators
1. Goldman adelilzation
2. Hecke operator operating on H^P (X, Γ, ρ) etc.
3. Hecke operator operating on Ω(X × F)
4. Hecke operators as algebraic correspondences
Chapter IV. Number theory of automorphic forms
1. A fibre variety over an algebraic curve U = Γ X
2. Harmonie forms on V, and the trace formulas
3. Zeta-function of widetilde{V}^p
4. Congruence Artin - L-functions
5. Hecke polynomials as L-functions
References for volume II: 1-17
18-43
44-69
70-95
