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SUMMARY; CHARSET=UTF-8 :The Grunwald Problem for solvable groups
UID:exeter_event_14244
URL:http://www.exeter.ac.uk/events/details/?event=14244
DTSTART;VALUE=DATE:20241009T133000
DTEND;VALUE=DATE:20241009T143000
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ORGANIZER: MAILTO:c.d.lazda@exeter.ac.uk
ATTACH: http://www.exeter.ac.uk/events/details/?event=14244
DTSTAMP:20240918T143125
LOCATION:Harrison Building 106 
DESCRIPTION; CHARSET=UTF-8 :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 $H^1(K,G) \to \prod_{v \in M_K} H^1(K_v,G)$. 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.http://www.exeter.ac.uk/events/details/?event=14244
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