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DTSTAMP:20260412T012547
DTSTART:20171006T160000
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URL:https://murmitoyen.com/events/vanille/udem/detail/785839-p-adic-analysi
 s-and-hilberts-twelfth-problem
LOCATION:Université de Montréal - Pavillon André-Aisenstadt\, 2920\, che
 min de la Tour\, Montréal\, QC\, Canada\, H3T 1N8
SUMMARY:p-adic Analysis and Hilbert's Twelfth Problem
DESCRIPTION:Conférence d'Henri Darmon
\nAbstractModular functions play an 
 important role in many aspects of number theory. The theory of complex mul
 tiplication\, one of the grand achievements of the subject in the 19th cen
 tury\, asserts that the values of modular functions at quadratic imaginary
  arguments generate (essentially all) abelian extensions of imaginary quad
 ratic fields. Hilbert's twelfth problem concerns the generalisation of thi
 s theory to other base fields. I will describe an ongoing work in collabor
 ation with Jan Vonk which identifies a class of functions that seem to pla
 y the role of modular functions for real quadratic fields. A key differenc
 e with the classical setting is that they are meromorphic functions of a p
 -adic variable (defined in the framework of 'rigid analysis' introduced by
  Tate) rather than of a complex variable. 
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