BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matt Broe (Boston University) DTSTART:20261006T200000Z DTEND:20261006T210000Z DTSTAMP:20261004T233531Z UID:FCNTS/39 DESCRIPTION:Title: T he Tate conjecture for abelian fourfolds over finite fields\nby Matt B roe (Boston University) as part of Five College Number Theory Seminar\n\nL ecture held in Seeley Mudd 207 @Amherst College.\n\nAbstract\nThe Tate con jecture describes the cohomology of algebraic varieties in terms of their geometry. In this talk\, I will discuss the proof of the Tate conjecture f or abelian fourfolds over finite fields. This is the first resolution of t he conjecture for all abelian varieties of a fixed dimension over finite f ields since the work of Tate in the 1960s. The argument relies on techniqu es from Ancona's proof of the standard conjecture of Hodge type for abelia n fourfolds\, and ultimately reduces to results of Markman on the Hodge co njecture for abelian varieties.\n\n\nCombining the above case of the Tate conjecture with theorems of Ancona and Kahn\, we deduce that the standard conjecture on homological versus numerical equivalence holds for abelian f ourfolds over arbitrary fields. This completes the proof of the standard c onjectures for abelian fourfolds.\n LOCATION:https://researchseminars.org/talk/FCNTS/39/ END:VEVENT END:VCALENDAR