# Celine Maistret (University of Bristol) - Parity of ranks of abelian surfaces

Dates: | 28 June 2022 |
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Times: | 14:00 - 15:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Speaker: | Celine Maistret |

Abstract : Let K be a number field and A/K an abelian surface. By the Mordell-Weil theorem, the group of K-rational points on A is finitely generated and as for elliptic curves, its rank is predicted by the Birch and Swinnerton-Dyer conjecture. A basic consequence of this conjecture is the parity conjecture: the sign of the functional equation of the L-series determines the parity of the rank of A/K. Assuming finiteness of the Shafarevich-Tate group, we prove the parity conjecture for principally polarized abelian surfaces under suitable local constraints. Using a similar approach we show that for two elliptic curves E_1 and E_2 over K with isomorphic 2-torsion, the parity conjecture is true for E_1 if and only if it is true for E_2.

### Speaker

Celine Maistret

Organisation: University of Bristol