Manchester Number Theory Seminar - Elvira Lupoian
| Dates: | 29 November 2022 |
|---|
| 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
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
