Seminar on Faltings's Theorem

Spring 2016
Mondays 9:30am-11:00am at SC 232

• Feb 19:30-11am SC 232Harvard Chi-Yun Hsu
  Tate's conjecture over finite fields and overview of Faltings's Theorem
  ([T1] and Ch 1,2 of [CS])
• Feb 129-10:30am SC 232Harvard Chi-Yun Hsu
  Introduction to group schemes ([T2] and Sec. 3.1-3.4 of [CS])
• Feb 159:30-11am SC 232Harvard Zijian Yao
  p-divisible groups ([T3] and Sec. 3.5-3.7 of [CS])
• Feb 229:30-11am SC 232Harvard Nicholas Triantafillou
  Basics of abelian varieties (Sec. 4.0-5.14 of [CS])
• Feb 299:30-11am SC 232Harvard Chi-Yun Hsu
  More on abelian varieties (Sec. 5.15-5.20 of [CS])
• Mar 79:30-11am SC 232Harvard Borys Kadets
  Height functions and Jacobians (Ch 6, 7 of [CS])
• Mar 149:30-11am SC 232Harvard No seminar - Arizona Winter School
  
• Mar 219:30-11am SC 232Harvard Alex Smith
  Néron models (Ch IV of [S], [BLR] and Ch 8 of [CS])
• Mar 289:30-11am SC 232Harvard Zijian Yao
  Arakelov intersection theory (Ch 12 of [CS] and [F])
• April 49:30-11am SC 232Harvard Chi-Yun Hsu
  Siegel moduli schemes and their compactification over C ([C], [G], [N] and Ch 9 of [CS])
• April 119:30-11am SC 232Harvard Alex Smith
  Proof of Faltings's theorem I: Overview (Ch 2 of [CS])
• April 189:30-11am SC 232Harvard Zijian Yao
  II: Tate's Conjecture implies Shafarevich's Conjecture (Sec. 2.6 of [CS])
• April 259:30-11am SC 232Harvard Koji Shimizu
  III: Shafarevich's Conjecture implies Mordell's Conjecture ([P] and Sec. 2.6 of [CS])
• April 279:30-11am SC 232Harvard Chi-Yun Hsu
  IV: Finiteness Theorem of Abelian Varieties with Bounded Heights ([D], [Sz1] and Sec. 2.2-2.3 of [CS])
• May 29:30-11am SC 232Harvard No seminar - Time conflict with Tasho's class this week
  
• May 99:30-11am SC 232Harvard Zijian Yao
  V: Isogenies and Heights ([D] and Sec. 2.4 of [CS])
• May 119:30-11am 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, p-divisible 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)