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SUMMARY:Elia Gorokhovsky (Harvard)
DTSTART:20250424T210000Z
DTEND:20250424T223000Z
DTSTAMP:20260422T220512Z
UID:STAGE/131
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/131/">
 The Kodaira--Parshin family</a>\nby Elia Gorokhovsky (Harvard) as part of 
 STAGE\n\nLecture held in Room 2-449 in the MIT Simons Building.\n\nAbstrac
 t\nIn this talk\, we describe the construction of an abelian-by-finite fam
 ily parametrized by a prime $q$ which is amenable to direct monodromy comp
 utations. This family\, the Kodaira-Parshin family\, serves as input to th
 e arguments in Section 6 which use an abelian-by-finite family with full m
 onodromy to prove finiteness of rational points. The bulk of the talk focu
 ses on the ``finite'' part of abelian-by-finite: we will describe the cons
 truction of an \\'etale cover of a curve $Y$ parametrizing $G$-covers of $
 Y$ branched at a single point\, together with a universal curve.\n\nRefere
 nce:\n\n$\\bullet$ <a href="https://link.springer.com/article/10.1007/s002
 22-020-00966-7">Lawrence and Venkatesh\, Diophantine problems and $p$-adic
  period mappings</a>\, Section 7.\n
LOCATION:https://researchseminars.org/talk/STAGE/131/
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