Seminar organised by Jinbi Jin (jinmengjun [plus] efg [at] gmail [dot] com)

In week 51, the seminar will be on Monday, 15:00-17:00, instead of the usual time.

Wednesday, 11:15-12:50, Room Sn401

This seminar will have two main goals. The first is to define the étale fundamental group of a connected scheme \(S\) using a categorical approach, and the second is to prove a finiteness theorem about étale fundamental groups of proper, connected schemes over an algebraically closed field \(k\). For these purposes, the following topics will be covered.

- Galois categories
- Finite étale morphisms of schemes
- Fibre functors; the étale fundamental group

- Descent
- GAGA (Géométrie Algébrique et Géométrie Analytique); Riemann Existence Theorem
- Specialisation theory for the étale fundamental group
- Chow's Lemma
- Bertini's Theorem

- A. Grothendieck,
*SGA I*→ arXiv.org - H. W. Lenstra,
*Galois theory for schemes*→ leidenuniv.nl

2 October | Jinbi Jin | Introduction |

9 October | Chloe Martindale | Galois Categories |

16 October | Maxim Mornev | Flat and Étale Morphisms I |

23 October | Maxim Mornev | Flat and Étale Morphisms II |

30 October | Milan Lopuhaä | The Galois Category of Finite Étale Coverings |

6 November | Wouter Zomervrucht | Faithfully Flat Descent |

13 November | Qijun Yan | Descent of Properties of Morphisms→ leidenuniv.nl |

20 November | --- | No seminar. |

27 November | Yan Zhao | GAGA |

4 December | Yan Zhao | Riemann Existence Theorem |

11 December | Jinbi Jin | Specialisation Theory |

16 December, 15:00-17:00 | Qijun Yan | ''Finiteness'' of the Étale Fundamental Group |