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UID:6070@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220428T110000
DTEND;TZID=Europe/Paris:20220428T120000
DTSTAMP:20241120T200906Z
URL:https://www.i2m.univ-amu.fr/evenements/valuation-of-coefficients-of-po
 lynomials-geometrically-realizing-gl_2z-nz/
SUMMARY:Zoé Yvon (I2M\, Aix-Marseille Université): Valuation of coefficie
 nts of polynomials geometrically realizing GL_2(Z/nZ)
DESCRIPTION:Zoé Yvon: The aim of the inverse Galois problem is to find fie
 lds extensions which Galois group is isomorphic to a given group. Here\, 
 we are interested in groups $\\mathrm{GL}_2(\\Z/n\\Z)$ where $n$ an integ
 er. We know that we can realize these groups as the Galois group of a gi
 ven number field $K$\, using the torsion points on an elliptic curve. Spe
 cifically\, a theorem of Reverter and Vila gives\, for each prime $n$\, a
  family of polynomials\, depending on an elliptic curve\, whose Galois gr
 oup is $\\mathrm{GL}_2(\\Z/n\\Z)$. We determine a lower bound on the val
 uations of the coefficients of these polynomials\, depending only on $n$\
 , when we take a short Weierstrass equation for the elliptic curve.\n\nSi
 te séminaire ATI : \nhttps://sites.google.com/view/samuele-anni/home/s%C
 3%A9minaire-ati\n\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/05/Zoe_Yvon.png
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
LOCATION:Luminy\, Campus des Sciences de Luminy\, Marseille\, 13009\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus des Sciences de Lumi
 ny\, Marseille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy:geo:0,0
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