David Zureick-Brown - Rational points and algebraic cycles

Random finite abelian groups
Idea
P(p | h(−D)) = P(p | #G) =
Let G p be the set of isomorphism classes of finite abelian groups of
p-power order.
Theorem (Cohen, Lenstra)
(i)
∑ 1
# Aut G = ∏ G∈G p i
(ii) G ↦→
(
1 − 1 p i ) −1
= C −1
p
C p
# Aut G is a probability distribution on G p
(iii) Avg (#G[p]) = Avg ( p rp(G)) = 2
David Zureick-Brown (Emory University) Random Dieudonné Modules November 13, 2012 6 / 29