Summer School 2022 -  Cohomology, Geometry and Explicit number theory (COGENT)

Collection Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Organizer(s) Institut Fourier, CNRS, UGA
Date(s) 13/06/2022 - 30/06/2022
linked URL https://if-summer2022.sciencesconf.org/
00:00:00 / 00:00:00
17 55

Brauer-Manin and cohomological obstructions to rational points

By Haowen Zhang

In the problem of deciding integer or rational solutions of polynomial equations (i.e. finding integer/rational points of a variety), we often first look at the “local” solutions over all the Q_p. When does a collection of local solutions give rise to an honest global solution over Q? There are necessary conditions given by certain cohomological groups like the Brauer group, and these conditions sometimes turn to be sufficient, defining the Brauer-Manin obstruction. We can also use such tools to study the problem of weak-approximation. Going beyond number fields, we can consider such problems of certain function fields of the shape C(X,Y), C((X,Y)), Q_p(X) etc and I’ll try to present some of my results on such problems.

Information about the video

  • Date of recording 28/06/2022
  • Date of publication 03/12/2025
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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