BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Asher Auel (Dartmouth College) DTSTART:20210318T163000Z DTEND:20210318T173000Z DTSTAMP:20260422T054046Z UID:SFUQNTAG/26 DESCRIPTION:Title: The local-global principle for quadratic forms over function fields\ nby Asher Auel (Dartmouth College) as part of SFU NT-AG seminar\n\n\nAbstr act\nThe Hasse-Minkowski theorem says that a quadratic form over a global field admits a nontrivial zero if it admits a nontrivial zero everywhere l ocally. Over more general fields of arithmetic and geometric interest\, th e failure of the local-global principle is often controlled by auxiliary s tructures of interest\, such as torsion points of the Jacobian and the Bra uer group. I will explain work with V. Suresh on the failure of the local -global principle for quadratic forms over function fields varieties of di mension at least two. The counterexamples we construct are controlled by higher unramified cohomology groups and involve the study of Calabi-Yau va rieties of generalized Kummer type that originally arose from number theor y. Along the way\, we need to develop an arithmetic version of a result o f Gabber on the nontriviality of certain unramified cohomology classes on products of elliptic curves.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/26/ END:VEVENT END:VCALENDAR