Instructor: Ching-Li Chai

Office: DRL 4N36, Ext. 8-8469.
Office Hours:

General Information

• First meeting: Friday 9/03, 10:15 am, online, zoom meeting ID 920 1348 6290, passcode 366472
  
  
• Lectures: MF 10:15--11:45 am, Fisher-Bennett 141, from the second meeting on.
  
  
• Topics: Abelian varieties, p-divisible groups and moduli spaces , including
  • Theorem of the cube, theorem of the square
  • Commutative finite group schemes, dual abelian varieties
  • Abelian schemes, descent, dual abelian schemes
  • p-divisible groups
  • Dieudonne theory over perfect fields of characteristic p>0
  • Abelian varieties over finite fields
  • Complex multiplication of abelian varieties
  • Moduli of abelian varieties, existence
  • Moduli abelian varieties of PEL type
  • Deformation of abelian varieties and p-divisible groups
  
  
  
• Background knowledge: graduate-level algebraic geometry
  
  
• References:
  • Books
    • Mumford, Abelian Varieties
    • Mumford, Geometric Invariant Theory, chapters 6-7
    • Ash-Mumford-Rapoport-Tai, Smooth Compactifications of Locally Symmetric Varieties, 1975
    • Demazure, Lectures on p-divisible groups, LNM 302
    • Messing, The Crystals Associated to Barsotti-Tate Groups with Applications to Abelian Schemes, LNM 264
    • Zink (in collaboration with Reimann) Cartiertheorie kommutativer formaler Gruppen, 1984, English translation available from the web.
    • Faltings-Chai, Degeneration of Abelian Varieties
    • Chai-Conrad-Oort, Complex Multiplication and Lifting Problems
  • Articles
    • Mumford, On the equations defining abelian varieties. I, 1966; II, III, 1967
    • Mumford, An analytic construction of degenerating abelian varieties, 1972
    • Mumford, Bi-extensions of formal groups, 1969
    • Manin, The theory of commutative formal groups, 1963
    • Deligne, Travaux de Shimura, Seminaire Bourbaki 1970/71
    • Illusie, Deformations de groupes de Barsotti-Tate, 1985
    • Chai-Oort, Moduli of abelian varieties and p-divisible groups, 2009, available from CLC's home page
    • Chai-Oort, Moduli of abelian varieties, 2018, available from CLC's web page
    • Zink, Lectures on p-divisible groups, available from the web.

Academic calendar fall 2021

• First day of classes, 8/31
• First meeting, Friday 9/03
• Drop period ends, 9/14
• Grade type change deadline, 10/29
• Fall break, 10/14--10/17
• Last day to withdraw, 11/08
• University Friday, Wednesday 11/24
• Thanksgiving break, 11/25--11/28
• Last day of classes, Friday 12/10