David Zureick-Brown - Rational points and algebraic cycles

More documents

Recommendations

Info

Proofs Part (iv) 1 st moment is 2: Avg (#G(F p )[p]) = 2 1 First fix the p-corank. 1 Associated p-divisible group decomposes as G = G m × G et × G ll . 2 Fixing the p-corank fixes the dimension of G ll 2 (Show that G random ⇒ G et random.) 3 G(F p ) = G et (F p ) = coker(F | M et − Id). 4 F | M et is random in GL g (Z p ). David Zureick-Brown (Emory University) Random Dieudonné Modules November 13, 2012 23 / 29
Proofs Part (v) P ( p ∤ # coker(F − Id)| F ∞ (M⊗F p)) = Cp . David Zureick-Brown (Emory University) Random Dieudonné Modules November 13, 2012 24 / 29
Page 1 and 2:
Random Dieudonné Modules and the C
Page 3 and 4:
Basic Question What is P(p | h(−D
Page 5 and 6:
Data (Buell ’76) P(p | h(−D))
Page 7 and 8:
Random finite abelian groups Idea P
Page 9 and 10:
Random finite abelian groups Idea P
Page 11 and 12:
Cohen and Lenstra’s conjecture Le
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Progress Davenport-Heilbronn - Avg
Page 19 and 20:
Cohen-Lenstra over F q (t), l ≠ p
Page 21 and 22:
Basic Question over F q (t), l ≠
Page 23 and 24: Main Tool over F q (t) - Tate Modul
Page 25 and 26: Main Tool over F q (t) - Tate Modul
Page 27 and 28: Random Tate-modules F ∈ GL 2g (Z
Page 29 and 30: Progress In the limit (w/ upper and
Page 31 and 32: Cohen-Lenstra over F p (t), l = p T
Page 33 and 34: Cohen-Lenstra over F p (t), l = p D
Page 35 and 36: Dieudonné Modules Definition (i) D
Page 41 and 42: Invariants via Dieudonné Modules I
Page 43 and 44: Main Theorem Theorem (Cais, Ellenbe
Page 51 and 52: Proofs Part (i) Mod pqp D has a nat
Page 57 and 58: Proofs Part (ii) P(a(M) = s) = p
Page 63 and 64: Proofs Part (iii) P(r(M) = g − s)
Page 69 and 70: Proofs Part (iv) 1 st moment is 2:
Page 71 and 72: Proofs Part (iv) 1 st moment is 2:
Page 73: Proofs Part (iv) 1 st moment is 2:
Page 77 and 78: Data, Moduli Spaces and Wild Specul
Page 83 and 84: C plane curve, p = 2 Theorem (Cais,
Page 85 and 86: a-number data Does P(a(Jac C (F p )
Page 91 and 92: Rational points on Moduli Spaces #H
Page 93 and 94: Rational points on Moduli Spaces #H
Page 95: Thank you Thank You! David Zureick-
show all

David Zureick-Brown - Rational points and algebraic cycles

Create successful ePaper yourself

Delete template?

Save as template?