BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stefan Kebekus (University of Freiburg) DTSTART:20210511T130000Z DTEND:20210511T140000Z DTSTAMP:20260423T021330Z UID:ZAG/119 DESCRIPTION:Title: Br auer-Manin obstruction on a simply connected fourfold and a Mordell theore m in the orbifold setting\nby Stefan Kebekus (University of Freiburg) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAlmost one decade ago\, Poonen constructed the first examples of algebraic varieties over global fields for which Skorobogatov's etale Brauer-Manin obstructio n does not explain the failure of the Hasse principle. By now\, several co nstructions are known\, but they all share common geometric features such as large fundamental groups. In this paper\, we construct simply connected fourfolds over global fields of positive characteristic for which the Bra uer-Manin machinery fails. Contrary to earlier work in this direction\, ou r construction does not rely on major conjectures. Instead\, we establish a new diophantine result of independent interest: a Mordell-type theorem f or Campana's "geometric orbifolds" over function fields of positive charac teristic. Along the way\, we also construct the first example of simply co nnected surface of general type over a global field with a non-empty\, but non-Zariski dense set of rational points. This is joint work with Jorge P ereira (IMPA) and Arne Smeets (Nijmegen)\n LOCATION:https://researchseminars.org/talk/ZAG/119/ END:VEVENT END:VCALENDAR