坂内健一研究室
発表記録 | ||
|---|---|---|
| 2011/11/25 | 小野 | 佐野 |
| 2011/11/11 | 小野 | 佐野 |
| 2011/11/04 | 小野 | |
| 2011/10/28 | ||
| 2011/10/14 | 木戸 | 佐野 |
| 2011/10/07 | 木戸 | 佐野 |
| 小野 | ||
| 2011/09/30 | 佐野 | 小野 |
発表記録 | ||
|---|---|---|
| 2011/09/09 | 大川 | 木戸 |
| 谷口 | ||
| 2011/09/02 | 大川 | |
| 2011/08/26 | 谷口 | 小野 |
| 佐野 | ||
| 2011/08/19 | 大川 | 木戸 |
| 2011/08/05 | 佐野 | |
| 2011/07/29 | 谷口 | 小野 |
| 2011/07/22 | 木戸 | 谷口 |
| 2011/07/15 | 佐野 | 木戸 |
| 2011/07/08 | 小野 | |
| 2011/06/24 | 木戸 | 谷口 |
| 2011/06/17 | 佐野 | 木戸 |
| 2011/06/10 | 小野 | 佐野 |
| 2011/06/03 | 谷口 | 小野 |
| 2011/05/27 | 木戸 | 谷口 |
| 2011/05/20 | 佐野 | 木戸 |
| 2011/05/13 | 小野 | 佐野 |
| 2011/05/06 | 佐野 | 谷口 |
| 2011/04/29 | 谷口 | 木戸 |
| 2011/04/22 | 小野 | 木戸 |
テキスト：J. Silverman, Arithmetic Theory of Elliptic Curves, GTM 106, Springer
Chapter I : Algebraic Varieties | ||
|---|---|---|
| §1.1 | Affine Varieties | 小野 |
| §1.2 | Projective Varieties | |
| §1.3 | Maps Between Varieties | 谷口 |
Chapter II : Algebraic Curves | ||
| §2.1 | Curves | 木戸 |
| §2.2 | Maps Between Curves | 佐野・谷口 |
| §2.3 | Divisors | 小野 |
| §2.4 | Differentials | 佐野・佐野 |
| §2.5 | The Riemann-Roch Theorems | 佐野 |
Chapter III : The Geometry of Elliptic Curves | ||
| §3.1 | Weierstrass Equations | 木戸・木戸 |
| 木戸 | ||
| §3.2 | The Groups Law | 谷口・谷口 |
| §3.3 | Elliptic Curves | 小野・小野 |
| §3.4 | Isogenies | 佐野・佐野 |
| 木戸・木戸 | ||
| §3.5 | The Invariant Differential | 谷口 |
| §3.6 | The Dual Isogeny | 小野 ・小野 |
| §3.7 | The Tate Module | 佐野 |
| §3.8 | The Weil Pairing | 木戸 ・木戸 |
| §3.9 | The Endomorphism Ring | 谷口 |
| §3.10 | The Automorphism Group | 谷口 |
Chapter IV : The Formal Group of an Elliptic Curve | ||
| §4.1 | Expansion Around $0$ | 小野 |
| §4.2 | Formal Groups | 小野 |
| §4.3 | Groups Associated to Formal Groups | 佐野 |
| §4.4 | The Invariant Differential | |
| §4.5 | The Formal Logarithm | 大川 |
| §4.6 | Formal Groups over Discrete Valuation Rings | 木戸 |
| §4.7 | Formal Groups in Characteristic $p$ | 谷口 |
Chapter V : Elliptic Curves over Finite Fields | ||
| §5.1 | Number of Rational Points | 小野 |
| §5.2 | The Weil Conjectures | 佐野 |
| §5.3 | The Endomorphism Ring | 大川 |
| §5.4 | Calculating the Hasse Invariant | |
Chapter VI : Elliptic Curves over $\mathbb{C}$ | ||
| §6.1 | Elliptic Integrals | 木戸 |
Chapter VII : Elliptic Curves over Local Fields | ||
| §7.1 | Minimal Weierstrass Equation | 佐野 |
| §7.2 | Reduction modulo $\pi$ | 小野 |
| §7.3 | Points of Finite Order | 木戸 |
| §7.4 | The Action of Inertia | |
| §7.5 | Good and Bad Reduction | 佐野 |
| §7.6 | The Group $E/E_0$ | 小野 |
| §7.7 | The Criterion of Néron-Ogg-Shafarevich | |
Chapter VIII : Elliptic Curves over Global Fields | ||
| §8.1 | The Weak Mordell-Weil Theorem | 木戸・佐野 |
| §8.2 | The Kummer Pairing via Cohomology | 小野 |
| §8.3 | The Descent Procedure | |
| §8.4 | The Mordell-Weil Theorem over $\mathbb{Q}$ | 木戸 |
| §8.5 | Heights on Projective Space | 小野・小野 |
| 小野 | ||
| §8.6 | Heights of Elliptic Curves | 佐野 |