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BEGIN:VEVENT
DTSTAMP:20220131T102614Z
DTSTART:20220215T150000Z
DTEND:20220215T160000Z
SUMMARY:Gabriel Dill (Oxford) - Around the support problem for Hilbert c
lass polynomials
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}x143-kz1e37
bn-raca7v
DESCRIPTION:Abstract : I will report on joint work in progress with Franc
esco Campagna. Let H_D(T) denote the Hilbert class polynomial of the ima
ginary 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 fo
r a and b belonging to various Dedekind domains. We also study the modul
ar support problem: if for all but finitely many D every prime ideal div
iding H_D(a) also divides H_D(b)\, what can we say about a and\nb? This
is inspired by work of Bugeaud-Corvaja-Zannier and Corrales-Rodrigáñez-S
choof\, 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 jo
int project with Campagna to study unlikely intersections in certain ari
thmetic varieties.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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