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The Grunwald Problem for solvable groups

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  • UserJulian Demeio (Bath)
  • ClockTuesday 12 November 2024, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jef Laga .

Let K be a number field. The Grunwald problem for a finite group (scheme) G/K asks what is the closure of the image of H1(K,G) → \prod_{v \in M_K} H1(K_v,G). For a general G, there is a Brauer—Manin obstruction to the problem, and this is conjectured to be the only one. In 2017, Harpaz and Wittenberg introduced a technique that managed to give a positive answer (BMO is the only one) for supersolvable groups. I will present a new fibration theorem over quasi-trivial tori that, combined with the approach of Harpaz and Wittenberg, gives a positive answer for all solvable groups.

This talk is part of the Number Theory Seminar series.

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