Gabriel Dill (Oxford) - Around the support problem for Hilbert class polynomials
| Dates: | 15 February 2022 |
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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, Adults, Alumni, Current University students |
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| Speaker: | Gabriel Dill |
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Abstract : I will report on joint work in progress with Francesco Campagna. Let H_D(T) denote the Hilbert class polynomial of the imaginary quadratic order of discriminant D. We study the rate of growth of the greatest common divisor of H_D(a) and H_D(b) as |D| \to \infty for a and b belonging to various Dedekind domains. We also study the modular support problem: if for all but finitely many D every prime ideal dividing H_D(a) also divides H_D(b), what can we say about a and
b? This is inspired by work of Bugeaud-Corvaja-Zannier and Corrales-Rodrigáñez-Schoof, who studied these questions with T^n-1 in place of H_D(T) in the ring of S-integers in some number field. It is also part of a longer joint project with Campagna to study unlikely intersections in certain arithmetic varieties.
Speaker
Gabriel Dill
Organisation: University of Manchester
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
