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SUMMARY:Alice Pozzi (UCL/CRM)
DTSTART:20201117T000000Z
DTEND:20201117T005000Z
DTSTAMP:20260423T041612Z
UID:UCLA_NTS/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/17/
 ">Derivatives of Hida families and rigid meromorphic cocycles</a>\nby Alic
 e Pozzi (UCL/CRM) as part of UCLA Number Theory Seminar\n\n\nAbstract\nA r
 igid meromorphic cocycle is a class in the first cohomology of the group\n
 $\\mathrm{SL}_2(\\mathbb{Z}[1/p])$ acting on the non-zero rigid meromorphi
 c functions on the Drinfeld\n$p$-adic upper half plane by Möbius transfor
 mation. Rigid meromorphic cocycles\ncan be evaluated at points of real mul
 tiplication\, and their values conjecturally\nlie in the ring class field 
 of real quadratic fields\, suggesting striking analogies\nwith the classic
 al theory of complex multiplication.\nIn this talk\, we discuss the relati
 on between the derivatives of certain $p$-adic\nfamilies of Hilbert modula
 r forms and rigid meromorphic cocycles. We explain\nhow the study of congr
 uences between cuspidal and Eisenstein families allows\nus to show the alg
 ebraicity of the values of a certain rigid meromorphic cocycle\nat real mu
 ltiplication points.\nThis is joint work with Henri Darmon and Jan Vonk.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/17/
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