Coleman integrals over number fields: a computational approach

Nirvana Coppola (Vrije Universiteit Amsterdam)

23-Feb-2022, 16:00-17:00 (2 years ago)

Abstract: One of the deepest mathematical results is Faltings's Theorem on the finiteness of rational points on an algebraic curve of genus $g \geq 2$. A much more difficult question, still not completely answered, is whether given a curve of genus $g \geq 2$, we can find all its rational points, or, more in general, all points defined over a certain number field. An entire (currently very active!) area of research is devoted to find an answer to such questions, using the "method of Chabauty".

In this seminar, I will talk about one of the first tools employed in Chabauty method, namely Coleman integrals, which Coleman used to compute an explicit bound on the number of rational points on a curve. After explaining how this is defined, I will give a generalisation of this definition for curves defined over number fields, and explain how to explicitly compute these integrals. This is based on an ongoing project, which started during the Arizona Winter School 2020, joint with E. Kaya, T. Keller, N. Müller, S. Muselli.

number theory

Audience: researchers in the topic


London number theory seminar

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Organizers: Caleb Springer*, Luis Garcia*
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