# Manchester Number Theory Seminar - Lilybelle Cowland Kellock

Dates: | 5 March 2024 |
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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: Lilybelle Cowland Kellock (UCL)

Title: A generalisation of Tate’s algorithm for hyperelliptic curves

Abstract: Tate's algorithm tells us that, for an elliptic curve E over a discretely valued field K with residue characteristic >= 5, the dual graph of the special fibre of the minimal regular model of E over K^{unr} can be read off from the valuation of j(E) and \Delta_E. This is really important for calculating Tamagawa numbers of elliptic curves, which are involved in the refined Birch and Swinnerton-Dyer conjecture formula. For a hyperelliptic curve C/K, we can ask if we can give a similar algorithm that gives important data related to the curve and its Jacobian from polynomials in the coefficients of a Weierstrass equation for C/K. This talk will be split between being an introduction to cluster pictures of hyperelliptic curves, from which the important data can be gathered, and a presentation of how the cluster picture can be recovered from polynomials in the coefficients of a Weierstrass equation.

Room: Frank Adams 1