# Level Raising mod 2 and Obstruction to Rank Lowering

@article{Li2019LevelRM, title={Level Raising mod 2 and Obstruction to Rank Lowering}, author={Chao Li}, journal={International Mathematics Research Notices}, year={2019}, volume={2019}, pages={2332-2355} }

Given an elliptic curve E defined over Q, we are motivated by the 2-part of the Birch and Swinnerton-Dyer formula to study the relation between the 2-Selmer rank of E and the 2Selmer rank of an abelian variety A obtained by Ribet’s level raising theorem. For certain imaginary quadratic fields K satisfying the Heegner hypothesis, we prove that the 2-Selmer ranks of E and A over K have different parity, as predicted by the BSD conjecture. When the 2-Selmer rank of E is one, we further prove that…

## 2 Citations

On the parity of the index of ramified Heegner divisors

- Mathematics
- 2019

Let E be an elliptic curve defined over the rationals and let N be its conductor. Assume N is prime. In this paper, we prove that the index on E of the Heegner divisor of discriminant $$D=-~4N$$D=-4N…

Quadratic Twists of Abelian Varieties With Real Multiplication

- MathematicsInternational Mathematics Research Notices
- 2019

Let $F$ be a totally real number field and $A/F$ an abelian variety with real multiplication (RM) by the ring of integers $\mathcal {O}$ of a totally real field. Assuming $A$ admits an $\mathcal…

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