Bar-Ilan Algebra Seminar
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Date: Wednesday, December 15, 2010 / 8 Tevet 5771
Time: 10:30 am promptly  
Place: Third floor seminar room, Mathematics building
 
Speaker: Tomer Schlank  (Hebrew University of Jerusalem)
 
Title: Homotopy theory and solubility of Diophantine equations
 
Abstract:
A classical problem in number theory is to determine  whether or not a
system of polynomial equations E has a rational solution.
If there is such a solution one can always present it. But to prove
that no solution exists might be a more delicate issue.
For this one uses the notion of obstructions.
 
In the talk I would present a way to construct such obstructions based
on exploring some kind of  topological realization of E  called  "The
\'{e}tale homotopy type", which was defined by Artin and Mazur. 
It turns out that this method of constructing obstructions can recover 
many of previously known obstructions (e.g the the Brauer -Manin, 
the \'{e}tale-Brauer and certain descent obstructions.) and thus give 
those obstructions  a topological interpretation
and shed light on the relationships between them.
 
This is  a joint work with Y.Harpaz.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Michael Schein   <mschein@math.biu.ac.il>