Seminar on Faltings's Theorem
Spring 2016
Mondays 9:30am11:00am at SC 232

Feb 19:3011am
SC 232Harvard
ChiYun Hsu
Tate's conjecture over finite fields and overview of Faltings's Theorem
([T1] and Ch 1,2 of [CS])

Feb 12910:30am
SC 232Harvard
ChiYun Hsu
Introduction to group schemes ([T2] and Sec. 3.13.4 of [CS])

Feb 159:3011am
SC 232Harvard
Zijian Yao
pdivisible groups ([T3] and Sec. 3.53.7 of [CS])

Feb 229:3011am
SC 232Harvard
Nicholas Triantafillou
Basics of abelian varieties (Sec. 4.05.14 of [CS])

Feb 299:3011am
SC 232Harvard
ChiYun Hsu
More on abelian varieties (Sec. 5.155.20 of [CS])

Mar 79:3011am
SC 232Harvard
Borys Kadets
Height functions and Jacobians (Ch 6, 7 of [CS])

Mar 149:3011am
SC 232Harvard
No seminar  Arizona Winter School

Mar 219:3011am
SC 232Harvard
Alex Smith
Néron models (Ch IV of [S], [BLR] and Ch 8 of [CS])

Mar 289:3011am
SC 232Harvard
Zijian Yao
Arakelov intersection theory (Ch 12 of [CS] and [F])

April 49:3011am
SC 232Harvard
ChiYun Hsu
Siegel moduli schemes and their compactification over C ([C], [G], [N] and Ch 9 of [CS])

April 119:3011am
SC 232Harvard
Alex Smith
Proof of Faltings's theorem I: Overview (Ch 2 of [CS])

April 189:3011am
SC 232Harvard
Zijian Yao
II: Tate's Conjecture implies Shafarevich's Conjecture (Sec. 2.6 of [CS])

April 259:3011am
SC 232Harvard
Koji Shimizu
III: Shafarevich's Conjecture implies Mordell's Conjecture ([P] and Sec. 2.6 of [CS])

April 279:3011am
SC 232Harvard
ChiYun Hsu
IV: Finiteness Theorem of Abelian Varieties with Bounded Heights ([D], [Sz1] and Sec. 2.22.3 of [CS])

May 29:3011am
SC 232Harvard
No seminar  Time conflict with Tasho's class this week

May 99:3011am
SC 232Harvard
Zijian Yao
V: Isogenies and Heights ([D] and Sec. 2.4 of [CS])

May 119:3011am
SC 232Harvard
Koji Shimizu
VI: Tate's Conjecture ([D], [Sz2] and Sec. 2.5 of [CS])
References:
[B] Bombieri, The Mordell Conjecture revisited (1990)
[BLR] Bosch, Lütkebohmert, Raynaud, Néron models
[D] Deligne, Preuve des conjectures de Tate et de Shafarevitch
[C] C.L. Chai, Moduli of abelian varieties (survey style)
[CS] Cornell, Silverman, Arithmetic Geometry
[P] Parshin, Algebraic curves over function fields (1968)
[F] Faltings, Calculus on arithmetic surfaces
[G] Goresky, Compactifications and cohomology of modular varieties
[HS] Hindry, Silverman, Diophantine Geometry
[L] Lang, Introduction to Arakelov Theory
[M] Milne, Abelian Varieties
[N] Namikawa, Toroidal compactification of Siegel spaces, LNM 812
[S] Silverman, Advanced Topics in the Arithmetic of Elliptic Curves
[Sz1] Szpiro, Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell
[Sz2] Szpiro, La conjecture de Mordell
[T1] Tate, Endomorphism of abelian varieties over finite fields (1966)
[T2] Tate, Finite flat group schemes
[T3] Tate, pdivisible groups
Related Papers:
Zarhin, Isogenies of abelian varieties over fields of finite characteristics (1974)
Zarhin, A remark on endomorphisms of abelian varieties over function fields of finite characterstics (1974)