BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Harry Smit (Max Planck Institute for Mathematics) DTSTART:20211006T150000Z DTEND:20211006T160000Z DTSTAMP:20260423T024610Z UID:hnts/37 DESCRIPTION:Title: Ch aracterizing number fields using L-series\nby Harry Smit (Max Planck I nstitute for Mathematics) as part of Heilbronn number theory seminar\n\n\n Abstract\nThe celebrated Neukirch-Uchida theorem states that two number fi elds with isomorphic absolute Galois group must be isomorphic themselves. This result has since been extended to quotients of this Galois group such as the solvable closure and (very recently\, by Saidi and Tamagawa) the 3 -step solvable closure. The abelianization does not\, however\, have this characterizing property. In fact\, many imaginary quadratic number fields have isomorphic abelianized Galois group.\n\nOne way to supplement the abe lianized Galois group is by adding some information on the (Dirichlet) L-s eries of the number fields. We show that in this way it is possible to not only characterize the number field\, but also the isomorphisms and homomo rphisms between number fields. If time allows\, we discuss how similar tec hniques can be used to characterize isogeny classes of abelian varieties u sing twists of the L-series attached to the abelian variety.\n LOCATION:https://researchseminars.org/talk/hnts/37/ END:VEVENT END:VCALENDAR