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SUMMARY:Edgar Costa (MIT)
DTSTART:20210422T210000Z
DTEND:20210422T220000Z
DTSTAMP:20260423T005824Z
UID:JNTS/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/22/">EF
 FECTIVE OBSTRUCTION TO LIFTING ALGEBRAIC CLASSES FROM POSITIVE CHARACTERIS
 TIC</a>\nby Edgar Costa (MIT) as part of Columbia CUNY NYU number theory s
 eminar\n\n\nAbstract\nWe will present two methods to compute upper bounds 
 on the number of algebraic cycles that lift from characteristic $p$ to cha
 racteristic zero. For an abelian variety\, we show that we can recover the
  decomposition of its endomorphism algebra from two well-chosen Frobenius 
 polynomials. We then focus on how to obtain similar bounds by relying on a
  single prime reduction\, and instead consider p-adic thickenings. More pr
 ecisely\, we show how to compute a $p$-adic approximation of the obstructi
 on map on the algebraic classes of a finite reduction for an abelian varie
 ty or a smooth hypersurface. This gives an upper bound on the “middle Pi
 card number” of a hypersurface or similarly an upper bound on the endomo
 rphism algebra or the Neron-Severi group of an abelian variety.\nThis is j
 oint work with: Davide Lombardo\, Nicolas Mascot\, Jeroen Sijsling\, Emre 
 Sertöz\, and John Voight.\n
LOCATION:https://researchseminars.org/talk/JNTS/22/
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