The p-parity conjecture for elliptic curves with a p-isogeny
Event details
| Date | 16.08.2012 |
| Hour | 11:15 › 12:30 |
| Speaker | Kestutis Cesnavicius |
| Location | |
| Category | Conferences - Seminars |
For an elliptic curve E over a number field K, one consequence of the Birch and Swinnerton-Dyer conjecture is the parity conjecture: the global root number
matches the parity of the Mordell-Weil rank. Assuming finiteness of the pprimary part of Sha(E/K) for a prime p, this is equivalent to the p-parity conjecture: the global root number matches the parity of the Z_p-corank of the pinfinity Selmer group. We prove the latter unconditionally for E that have a Krational p-isogeny. We deduce that the p-parity conjecture holds for every E with complex multiplication defined over K, and that for such E, if the p-primary part of Sha(E/K) is infinite, it must contain (Q_p/Z_p)^2.
matches the parity of the Mordell-Weil rank. Assuming finiteness of the pprimary part of Sha(E/K) for a prime p, this is equivalent to the p-parity conjecture: the global root number matches the parity of the Z_p-corank of the pinfinity Selmer group. We prove the latter unconditionally for E that have a Krational p-isogeny. We deduce that the p-parity conjecture holds for every E with complex multiplication defined over K, and that for such E, if the p-primary part of Sha(E/K) is infinite, it must contain (Q_p/Z_p)^2.
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Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii