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SUMMARY:Ratko Darda (Paris University (Paris 7))
DTSTART:20210219T133000Z
DTEND:20210219T143000Z
DTSTAMP:20260423T023053Z
UID:zorp_1729/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zorp_1729/5/
 ">Manin conjecture for algebraic stacks</a>\nby Ratko Darda (Paris Univers
 ity (Paris 7)) as part of ZORP (zoom on rational points)\n\n\nAbstract\nWe
  study the conjecture of Manin--Batyrev--Peyre in the context of algebraic
  stacks.\nTwo examples are of particular interest: the compactification of
  the moduli stack of elliptic curves $\\overline{ \\mathcal{M}_{1\,1}} $ a
 nd the classifying stack $ BG $ for $ G $  finite group\, which classifies
  $G$-torsors. The stack $\\overline{ \\mathcal{M}_{1\,1}} $ is isomorphic 
 to the weighted projective stack $\\mathcal{P}(4\, 6)$\nwhich is the quoti
 ent stack for the weighted action of $\\mathbb{G}_m$ on $\\mathbb{A}^2\\se
 tminus\\{0\\}$  with weights $4\, 6$. For weighted projective stacks\, we 
 define heights that we can use for counting\nits rational points\, example
 s are given by the naive height and the Faltings’ height\nof an elliptic
  curve.\n\nWe try to motivate why the second example may help us obtain a 
 geometrical reinterpretation of constants appearing in Malle conjecture\, 
 which predicts the number of Galois extensions with fixed Galois group $G$
 .\n
LOCATION:https://researchseminars.org/talk/zorp_1729/5/
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