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UID:2103@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20180109T140000
DTEND;TZID=Europe/Paris:20180109T150000
DTSTAMP:20171225T130000Z
URL:https://www.i2m.univ-amu.fr/evenements/iwasawa-algebras-of-p-adic-lie-
 groups-and-galois-representations-with-open-image/
SUMMARY: (...): Iwasawa algebras of p-adic Lie groups and Galois representa
 tions with open image
DESCRIPTION:: A key tool in the study of algebraic number fields are Iwasaw
 a algebras\, originally constructed by Iwasawa in the 1960s to study the "
 class groups" of fields\, but  since appearing in varied settings such as 
 a Lazard’s work on p-adic Lie groups and Fontaine’s work on local Galo
 is representations. For a prime p\, the Iwasawa algebra of a p-adic Lie gr
 oup G\, denoted by Zp[[G]]\, is a non-commutative completed group  algebra
  of G. In the first part of the talk\, we lay the foundation by giving a v
 ery explicit description of certain Iwasawa algebras (one such algebra was
  described by my advisor Clozel). The base change map between the Iwasawa 
 algebras over extensions of Qp motivates us to discuss globally analytic p
 -adic representations following Emerton’s work. In the second part of th
 e talk\, we will discuss about numerical  experiments using a computer alg
 ebra system which give heuristic support to Greenberg’s p-rationality co
 njecture which affirms the existence of “p-rational” number fields wit
 h Galois groups (Z/2Z)^t. The p-rational fields are algebraic number field
 s whose Galois cohomology is particularly simple and which are interesting
  because they offer ways of constructing Galois representations with big o
 pen images. We go beyond Greenberg’s work and construct novel Galois rep
 resentations of the absolute Galois group of Q with big open images in red
 uctive groups over Zp  (ex. GL(n\; Zp)\; SL(n\;Zp)\; SO(n\; Zp)\; Sp(2n\; 
 Zp)). We are proving results which show the existence of p-adic Lie extens
 ions of Q where the Galois group corresponds to a certain specific p-adic 
 Lie algebra (ex. sl(n)\; so(n)\; sp2n). This relates our work with a more 
 general and classical Inverse Galois problem for p-adic Lie extensions.htt
 p://sites.google.com/site/rayjishnu1992/
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DTSTART:20171029T020000
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