# SCHEDULE

For references, click on References Tab for more info.

Let's thank Holden Lee for graciously sharing his typed notes.

Date | Topic | Reference | Remark |
---|---|---|---|

09-06 | definition of group schemes | [Mum] sec 11 (pp.89-91,96-98), [BLR] 4.1, etc | |

09-11 | quotients by group schemes 1 | [vdGM] sec 4, [MFK] sec 0.1-0.4, cf. [Mum] sec 7, 12 | Geom quot in [vdGM] are a little different from those in [MFK]. I followed [vdGM]. |

09-13 | quotients by group schemes 2 | [vdGM] Th 4.16, [Mum] sec 12 | |

09-18 | equivariant sheaves | [Mum] sec 12, [MFK] sec 1.3, [Vis] sec 3.8 | [Vis] is for generalists as it discusses equivariant objects in a category. |

09-20 | definition of abelian schemes | [MFK] pp.115-117, [Lan] 1.3.1.1-1.3.1.8, [Mum] sec 4 | |

09-25 | rigidity lemma, isogenies | [MFK] Prop 6.1, Lem 6.12, [Lan] 1.3.1.9-1.3.1.13 | |

09-27 | more on isogenies, theorem of the cube | [Mum] sec 6, [vdGM] sec 2 | narrow focus to ab. var. over fields for a while |

10-02 | Th of square, Seesaw and K(L) | [Mum] sec 6, 10; start of sec 13 discusses K(L) [vdGM] sec 2 | Seesaw => Th of cube is in [Mum] sec 10. It's a nice proof to read. |

10-04 | Projectivity, rank of A[n] | [Mum] sec 6, [vdGM] sec 2, 5 | see [Mil] Th 7.1 for reduction to alg closed and another proof of projectivity. |

10-09 | MIT holiday (no class) | ||

10-11 | Picard schemes, dual abelian schemes | [BLR] Ch 8, [MFK] p.120, [Kle], [FC] pp.2-7 | |

10-16 | No class, hooray! | SWS is out of town (to Fields Inst.) | |

10-18 | Duality continued | [Mum] sec 13, [vdGM] sec 7.2 | Black boxes are [Mum] sec 12, thm 2; sec 13, cor 1,2. |

10-23 | Poincare reducibility, Cartier duality | [Mum] thm 19.1, sec 14, [vdGM] thm 12.2, sec 3.22 | |

10-25 | ker of dual isogeny, Tate modules | [Mum] thm 15.1, sec 18 [vdGM] thm 7.5, sec 10 | |

10-30 | Hom, End and deg function | [Mum] sec 19 | |

11-01 | characteristic poly | [Mum] sec 19-20 | |

11-06 | Riemann forms | [Mum] sec 20 | |

11-08 | Rosati involution | [Mum] sec 20-21 | |

11-13 | Complex abelian varieties | [Mum] sec 1-3, 9, 24 | |

11-15 | CM abelian varieties | [Mum] sec 22, [Mil3] sec 2,3,6,7 [Mil4] sec 1, [ST] | See "Remarks" page for Zariski density of l-power torsions. |

11-20 | End algebra over finite fields, I | [Tat4], [Mum] Appendix A | |

11-22 | Happy Thanksgiving! | ||

11-27 | End algebra over finite fields, II | [Tat4], [Mum] Appendix A | |

11-29 | Finite group schemes over a field of char p | [Gro] I.5-II.3, [Tat3], [Mum] sec 14 | |

12-04 | Dieudonne theory, p-divisible groups | [Gro] I.1-4,II.4,III.5, [Tat1], [Dem] Ch 3 | |

12-06 | class holiday | SWS is away to Berkeley | |

12-11 | Honda-Tate theory | [Tat2], [MW], [Dem] Ch 4 |