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Higher Ramanujan Equations and Periods of Abelian Varieties
| Softcover ISBN: | 978-1-4704-6019-8 |
| Product Code: | MEMO/281/1391 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-7324-2 |
| Product Code: | MEMO/281/1391.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-6019-8 |
| eBook: ISBN: | 978-1-4704-7324-2 |
| Product Code: | MEMO/281/1391.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
| AMS Member Price: | $136.00 $102.00 |
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Higher Ramanujan Equations and Periods of Abelian Varieties
| Softcover ISBN: | 978-1-4704-6019-8 |
| Product Code: | MEMO/281/1391 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-7324-2 |
| Product Code: | MEMO/281/1391.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-6019-8 |
| eBook ISBN: | 978-1-4704-7324-2 |
| Product Code: | MEMO/281/1391.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
| AMS Member Price: | $136.00 $102.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 281; 2023; 125 ppMSC: Primary 14; 37; 11
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Table of Contents
-
Chapters
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Introduction
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Terminology and conventions
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Acknowledgments
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1. The arithmetic theory of the higher Ramanujan equations
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1. Symplectic vector bundles over schemes
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2. Symplectic-Hodge bases of principally polarized abelian schemes
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3. Abelian schemes with real multiplication
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4. The moduli stacks $\mathcal {B}_g$ and $\mathcal {B}_F$
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5. The tangent bundles of $\mathcal {B}_g$ and $\mathcal {B}_F$; higher Ramanujan vector fields
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6. Integral solution of the higher Ramanujan equations
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7. Representability of $\mathcal {B}_g$ and $\mathcal {B}_F$ by a scheme
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8. The case of elliptic curves: explicit equations
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2. The analytic higher Ramanujan equations and periods of abelian varieties
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9. Analytic families of complex tori, abelian varieties, and their uniformization
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10. Analytic moduli spaces of complex abelian varieties with a symplectic-Hodge basis
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11. The analytic higher Ramanujan equations
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12. Values of $\varphi _g$ and $\varphi _F$; periods of abelian varieties
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13. An algebraic independence conjecture on the values of $\varphi _F$
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14. Group-theoretic description of the higher Ramanujan vector fields
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15. Zariski-density of leaves of the higher Ramanujan foliation
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A. Gauss-Manin connection on some families of elliptic curves
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Index of notation
-
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
Volume: 281; 2023; 125 pp
MSC: Primary 14; 37; 11
-
Chapters
-
Introduction
-
Terminology and conventions
-
Acknowledgments
-
1. The arithmetic theory of the higher Ramanujan equations
-
1. Symplectic vector bundles over schemes
-
2. Symplectic-Hodge bases of principally polarized abelian schemes
-
3. Abelian schemes with real multiplication
-
4. The moduli stacks $\mathcal {B}_g$ and $\mathcal {B}_F$
-
5. The tangent bundles of $\mathcal {B}_g$ and $\mathcal {B}_F$; higher Ramanujan vector fields
-
6. Integral solution of the higher Ramanujan equations
-
7. Representability of $\mathcal {B}_g$ and $\mathcal {B}_F$ by a scheme
-
8. The case of elliptic curves: explicit equations
-
2. The analytic higher Ramanujan equations and periods of abelian varieties
-
9. Analytic families of complex tori, abelian varieties, and their uniformization
-
10. Analytic moduli spaces of complex abelian varieties with a symplectic-Hodge basis
-
11. The analytic higher Ramanujan equations
-
12. Values of $\varphi _g$ and $\varphi _F$; periods of abelian varieties
-
13. An algebraic independence conjecture on the values of $\varphi _F$
-
14. Group-theoretic description of the higher Ramanujan vector fields
-
15. Zariski-density of leaves of the higher Ramanujan foliation
-
A. Gauss-Manin connection on some families of elliptic curves
-
Index of notation
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.