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Torsors and Topology in Diophantine Equations

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Speaker: 
David Corwin
Zugehörigkeit: 
MSRI Berkeley/MPIM
Datum: 
Don, 2021-08-26 15:00 - 16:00
Parent event: 
MPI-Oberseminar

https://zoom.us/j/93172910947
Meeting ID: 931 7291 0947
For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

Solutions to Diophantine equations (aka rational and integral points on varieties) may be studied using a variety of methods. I’ll survey some of the ways that Galois theory (of the rationals) and topology (of the complex manifold underlying the variety) may be used for that purpose. A key notion relating rational points to Galois theory and topology is the Galois-equivariant torsor(s) associated to a rational point. After going over the basic idea, I’ll indicate how this comes up in two of my research areas: 1) obstructions to the local-global (Hasse) principle, and 2) non-abelian Chabauty’s method.

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