David Zureick-Brown - Rational points and algebraic cycles
David Zureick-Brown - Rational points and algebraic cycles
David Zureick-Brown - Rational points and algebraic cycles
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Cohen <strong>and</strong> Lenstra’s conjecture<br />
Let f : G p → Z be a function.<br />
Definition<br />
Avg f = ∑<br />
G∈G p<br />
C p<br />
# Aut G · f (G)<br />
Avg Cl f =<br />
∑<br />
0≤D≤X f (Cl(−D) p)<br />
∑<br />
0≤D≤X 1<br />
Conjecture (Cohen, Lenstra)<br />
(i) Avg Cl f = Avg f<br />
(ii) Avg (# Cl(−D)[p]) 2 = 2 + p<br />
(iii) P(Cl(−D) p<br />
∼ = G) =<br />
C p<br />
# Aut G .<br />
<strong>David</strong> <strong>Zureick</strong>-<strong>Brown</strong> (Emory University) R<strong>and</strong>om Dieudonné Modules November 13, 2012 7 / 29
Change language