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SUMMARY:Hélène Esnault (Freie Universität Berlin)
DTSTART:20200714T140000Z
DTEND:20200714T150000Z
DTSTAMP:20260423T021451Z
UID:ZAG/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/31/">Den
 sity of arithmetic representations</a>\nby Hélène Esnault (Freie Univers
 ität Berlin) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra
 ct\nThe  lecture surveys recent work with Moritz Kerz. The motivation is t
 he conjecture that the  Hard-Lefschetz (HL) property holds on smooth proje
 ctive varieties defined over algebraically closed  char. $p>0$ fields for 
 cohomology with values in  semi-simple $\\ell$-adic local systems $V$. We 
 know it is true if $V$ comes from geometry (Deligne\, Beilinson-Bernstein-
 Deligne-Gabber) by Deligne’s theory of weights. In absence of weights\, 
 we proved it if $V$ has rank $1$ and reduced the whole HL conjecture to a 
 density conjecture on arithmetic semi-simple $\\ell$-adic systems on $P^1$
  minus $3$ closed points\, which we can prove in rank $2$.\n
LOCATION:https://researchseminars.org/talk/ZAG/31/
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