# Manchester Number Theory Seminar - Elvira Lupoian

Dates: | 29 November 2022 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

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

Speaker: Elvira Lupoian (University of Warwick)

Title: Two-Torsion Subgroup of Jacobians of Genus 5 Curves

Abstract: Let C be a smooth, projective and non-hyperelliptic curve of genus 5 over Q and let J be its Jacobian. Recall that J is a 5-dimension abelian variety whose points can be identified with elements of the zero Picard group of C. The Mordell-Weil theorem states that for any number field L, J(L) is a finitely generated group; that is, J(L) = J(L)_{tors} \oplus Z^r, where J(L)_{tors} is a finite group, the torsion subgroup, and r >= 0 is the rank. In this talk I will present a method of computing the 2-torsion subgroup of J; that is the group J[ 2 ] = { P \in J(Qbar) | 2P = 0 }, and hence the 2-torsion over any number field L.

This method was used to verify the Generalized Ogg conjecture for X_0(N) with N = 42, 55, 63, 72, 75.

Room: Frank Adams 1