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SUMMARY:Lue Pan (Princeton)
DTSTART:20220126T170000Z
DTEND:20220126T182000Z
DTSTAMP:20260423T035752Z
UID:RAMpAGe/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/65/"
 >On the p-adic Hodge structure of completed cohomology of modular curves I
 I</a>\nby Lue Pan (Princeton) as part of Recent Advances in Modern p-Adic 
 Geometry (RAMpAGe)\n\n\nAbstract\nLet $p$ be a prime. I plan to explain ho
 w to read the $p$-adic Hodge structure of the $p$-adically completed cohom
 ology of modular curves by studying the $p$-adic geometry of the modular c
 urves at infinite level. One main tool is the relative Sen theory (also ca
 lled $p$-adic Simpson correspondence) which provides a first-order differe
 ntial equation and allows us to apply differential operators pulled back f
 rom the flag variety along the Hodge-Tate period map.\n\nLecture (1): Hodg
 e-Tate structure\nLecture (2): de Rham structure\n\nIf time permits\, I wi
 ll also discuss several applications.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/65/
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