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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Galois theory of q-difference in the roots of unit
y - Hardouin\, C (Heidelberg)
DTSTART;TZID=Europe/London:20090515T093000
DTEND;TZID=Europe/London:20090515T103000
UID:TALK18399AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18399
DESCRIPTION:For $q in mathbb{C}*$ non equal to $1$\, we denote
by $ igma_q$ the automorphism of $mathbb{C}(z)$ g
iven by $ igma_q(f)(z)=f(qz)$. As q goes to $1$\,
a q-difference equation w.r.t. $ igma_q$ goes to a
differential equation. The theory related to this
fact is also called extit{confluence} and one pa
rt of its study is the behaviour of the related Ga
lois groups during this process. Therefore it seem
s interresting to have a good Galois theory of q-d
ifference equation for q equal to a root of unity.
Because of the increasing size of the constant fi
eld at these points\, such construction has been a
voided for a long time. Recently P.Hendricks has p
roposed a solution to this problems but his Galois
groups were defined over very transcendant fields
. We propose here a new approach based\, in a cert
ain sense\, on a q-deformation of the work of B.H.
Matzat and Marius van der Put for Differential Ga
lois theory in positive characteristic. We conside
r also a family of extit{iterative difference ope
rator} instead of considering\, just one differenc
e operator\, and by this way we stop the increasin
g of the constant field and succeed to set up a Pi
card-Vessiot Theory for q-difference equations whe
re q is a root of unity and relate it to a Tannaki
an approach.
LOCATION:Satellite
CONTACT:Mustapha Amrani
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