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SUMMARY:Ratko Darda (University of Osaka)
DTSTART:20220118T084000Z
DTEND:20220118T091000Z
DTSTAMP:20260423T010920Z
UID:JENTE/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/66/">M
 anin-Peyre conjecture for weighted projective stacks</a>\nby Ratko Darda (
 University of Osaka) as part of Japan Europe Number Theory Exchange Semina
 r\n\n\nAbstract\nManin-Peyre conjecture predicts the number of rational po
 ints of bounded height on algebraic varieties. The constants appearing in 
 the prediction are expressed using arithmetic and geometric invariants of 
 the variety. It is natural to ask if the constants appearing in some other
  arithmetic counting results\, like counting elliptic curves of bounded na
 ive or Faltings height or counting Galois extensions with fixed Galois gro
 up G of bounded discriminant\, could be explained in a similar way. But th
 ese objects are not parametrized by a variety but by an algebraic stack. I
 n this talk\, we will be focused on weighted projective stacks (the stacky
  quotients (A^n-{0})/Gm for a weighted action)\, when a complete theory of
  Manin-Peyre conjecture can be provided. This explains all the constants f
 or the elliptic curves and some of the constants when G=\\mu_m is the grou
 p of m-th roots of unity.\n
LOCATION:https://researchseminars.org/talk/JENTE/66/
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