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SUMMARY:Alice Pozzi (Imperial College London)
DTSTART:20201203T233000Z
DTEND:20201204T003000Z
DTSTAMP:20260423T005721Z
UID:UCSBsga/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSBsga/2/">
 Derivatives of Hida families and rigid meromorphic cocycles</a>\nby Alice 
 Pozzi (Imperial College London) as part of UCSB Seminar on Geometry and Ar
 ithmetic\n\n\nAbstract\nA rigid meromorphic cocycle is a class in the firs
 t cohomology of the group ${\\rm SL}_2(\\mathbb{Z}[1/p])$ acting on the no
 n-zero rigid meromorphic functions on the Drinfeld $p$-adic upper half pla
 ne by Mobius transformation. Rigid meromorphic cocycles can be evaluated a
 t points of real multiplication\, and their values conjecturally lie in th
 e ring class field of real quadratic fields\, suggesting striking analogie
 s with the classical theory of complex multiplication.\n\nIn this talk\, w
 e discuss the relation between the derivatives of certain $p$-adic familie
 s of Hilbert modular forms and rigid meromorphic cocycles. We explain how 
 the study of congruences between cuspidal and Eisenstein families allows u
 s to show the algebraicity of the values of a certain rigid meromorphic co
 cycle at real multiplication points.\n\nThis is joint work with Henri Darm
 on and Jan Vonk.\n
LOCATION:https://researchseminars.org/talk/UCSBsga/2/
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