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SUMMARY:Xinyu Zhou (Boston University)
DTSTART:20250227T220000Z
DTEND:20250227T233000Z
DTSTAMP:20260422T220656Z
UID:STAGE/125
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/125/">
 Families of varieties with good reduction</a>\nby Xinyu Zhou (Boston Unive
 rsity) as part of STAGE\n\nLecture held in Room 2-449 in the MIT Simons Bu
 ilding.\n\nAbstract\nWe review some constructions on crystalline represent
 ations and cohomology. Then we present a result in Lawrence-Venkatesh that
  shows the points in a residue disk that define semisimple representations
  are contained in a proper analytic subset. The proof illustrates the basi
 c strategy in Lawrence-Venkatesh: to show the finiteness of a set of point
 s\, one only need to show its image in the period domain is contained in a
  Zariski-closed subset with dimension smaller than that of the orbit of a 
 point under the complex monodromy group.\n\nReference:\n\n$\\bullet$ <a hr
 ef="https://link.springer.com/article/10.1007/s00222-020-00966-7">Lawrence
  and Venkatesh\, Diophantine problems and $p$-adic period mappings</a>\, S
 ection 3.\n\n$\\bullet$ <a href="https://mathscinet.ams.org/mathscinet/art
 icle?mr=1463696">Faltings\, Crystalline cohomology and p-adic Galois-repre
 sentations.</a> Algebraic analysis\, geometry\, and number theory (Baltimo
 re\, MD\, 1988)\, 25–80.\n\n$\\bullet$ <a href="http://www.ams.org/books
 /pspum/055.1/"> Illusie\, Crystalline cohomology.</a> Section 3.Motives (S
 eattle\, WA\, 1991)\, 43–70.\n
LOCATION:https://researchseminars.org/talk/STAGE/125/
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