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SUMMARY:Ambrus Pal (Imperial)
DTSTART:20231025T150000Z
DTEND:20231025T160000Z
DTSTAMP:20260418T065926Z
UID:LNTS/114
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/114/">T
 ate's conjecture for certain Drinfeld modular surfaces</a>\nby Ambrus Pal 
 (Imperial) as part of London number theory seminar\n\nLecture held in Room
  140\, the Huxley Building\, Imperial College London.\n\nAbstract\nTate's 
 conjecture on algebraic cycles is one of the central conjectures in arithm
 etic geometry\, but it is open even for codimension one cycles. There are 
 only a few classes of varieties when this claim is known. I will report ab
 out a new class of surfaces defined over global function fields which were
  defined by Stuhler in there original form\, and are closely analogous to 
 Hilbert modular surfaces. Our proof employs p-adic methods\, including the
  p-adic Lefschetz (1\,1) theorem proved by Lazda and myself. We also explo
 it that these varieties are totally degenerate in the sense of Raskind\, b
 ut this is not sufficient\, we need some information from the Langlands co
 rrespondence\, too. I will also talk about some particularly simple surfac
 es which show that the first property cannot be used to give a quicker pro
 of. Joint work with Koskivirta.\n
LOCATION:https://researchseminars.org/talk/LNTS/114/
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