# Formal groups 2 (Algebraic Number Theory IV)

The main topics of the course will be (finite flat) group schemes, $p$-divisible groups and descriptions of (categories of) $p$-divisible groups in terms of “linear algebra”, such as Dieudonné theory and/or Grothendieck-Messing theory.

In a sense, this course will be a continuation of the Course on formal groups of the previous term, but we will sort of start from scratch so that you can actually join in without knowing anything about formal group laws.

**Schedule:** Tue, 8:30-10:00 (S-U-4.02); Wed 10-12 (S-U-3.02). Exercise group: Mon, 2-4pm, O-3.46 (first session May, 8).

## Problem sheets

Download | Due date | |

1 | pdf (updated May 16) | May 3 |

2 | May 10 | |

3 | May 17 | |

4 | May 24 | |

5 | May 31 | |

6 | June 7 | |

7 | June 14 | |

8 | June 21 | |

9 | June 28 | |

10 | July 5 | |

11 | July 12 | |

12 | July 19 |

## Main References

J.-M. Fontaine, Groupes $p$-divisibles sur les corps locaux, Astérisque **47-48** (1977)

R. Pink, Finite group schemes, Lecture Notes

## Further Reading

M. Demazure, Lectures on $p$-divisible groups, Springer Lecture Notes in Math. **302**

B. Edixhoven, G. van der Geer, B. Moonen, Abelian varieties, in particular Ch. 3, Ch. 4.

W. Messing, The crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Springer LNM 264 (1972)

D. Mumford, Abelian Varieties, Tata Inst./Oxford Univ. Press, in particular §§ 7, 11, 12.

S. Shatz, Group Schemes, Formal Groups, and $p$-divisible Groups, in: Cornell, Silverman (eds.), Arithmetic Geometry, Springer 1986

J. Stix, A course on finite flat group schemes and $p$-divisible groups, Lecture Notes

J. Tate, Finite flat group schemes, in: Cornell, Silverman, Stevens (eds.), Modular Forms and Fermat’s Last Theorem, Springer 1997