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SUMMARY:Kenta Suzuki (MIT)
DTSTART:20250508T193000Z
DTEND:20250508T210000Z
DTSTAMP:20260422T220708Z
UID:STAGE/133
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/133/">
 Monodromy of the Kodaira--Parshin family</a>\nby Kenta Suzuki (MIT) as par
 t of STAGE\n\nLecture held in Room 4-149\, in the Maclaurin Buildings.\n\n
 Abstract\nWe complete the final step of the proof\, proving that the monod
 romy of the Kodaira-Parshin family is large. Let $Y$ be a compact orientab
 le surface or genus $g\\ge 2$ and let $Y^0$ be the puncture at a point. Le
 t $(Z_1\,\\pi_1)\,\\dots\,(Z_N\,\\pi_N)$ be the $\\mathrm{Aff}(q)$-covers 
 of $Y^0$\, and let $\\mathrm{MCG}(Y^0)_0$ be those mapping classes of $Y^0
 $ who induce trivial mapping classes on every $Z_i$. Then $\\mathrm{MCG}(Y
 ^0)_0$ acts on the primitive homomology $H_1^{\\mathrm{Pr}}(Z_i\,Y^0)$ of 
 $Z_i$\, i.e.\, the orthogonal complement of $\\pi_i^*H_1(Z_i)\\subset H_1(
 Y^0)$. We prove that $\\mathrm{MCG}(Y^0)_0\\to\\prod_{i=1}^N\\mathrm{Sp}(H
 _1^{\\mathrm{Pr}}(Z_i\,Y^0))$ has Zariski dense image.\n\nBy Goursat's lem
 ma it suffices to prove each $\\mathrm{MCG}(Y^0)_0\\to\\mathrm{Sp}(H_1^{\\
 mathrm{Pr}}(Z_i\,Y^0))$ has Zariski dense image\, which we prove by produc
 ing many Dehn twists on $Y^0$ inducing trivial mapping classes on $Z_i$.\n
 \nReference:\n\n$\\bullet$ <a href="https://link.springer.com/article/10.1
 007/s00222-020-00966-7">Lawrence and Venkatesh\, Diophantine problems and 
 $p$-adic period mappings</a>\, Section 8.\n
LOCATION:https://researchseminars.org/talk/STAGE/133/
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