Manchester Number Theory Seminar - Ilaria Cruciani
| Dates: | 7 October 2025 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Ilaria Cruciani (Roma Tre/Manchester)
Title: Finiteness in powers of elliptic schemes over cyclotomic extensions
Abstract: A central theme in number theory is understanding when sets of rational or algebraic points on varieties are finite or infinite. Classical results, such as Northcott’s theorem, show that imposing bounds on both the degree and the height of points over number fields guarantees finiteness. More subtle phenomena arise when one allows infinite extensions of a number field, for example the cyclotomic closure, which contains all roots of unity. A fundamental result of Serre states that an elliptic curve defined over a number field has only finitely many torsion points over the cyclotomic closure, despite this being an infinite extension. In this talk, I will present relative and higher-dimensional analogues inspired by Serre’s theorem for elliptic schemes, and explore their connections with Unlikely Intersections and the Zilber-Pink conjecture.
Room: Frank Adams 1
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Frank Adams 1
Alan Turing Building
Manchester
