1422

Date | Jan 09, 2015 |
---|---|

Speaker | Luc Illusie |

Dept. | University of Paris |

Room | 27-220 |

Time | 14:00-15:30 |

I will explain the key points in the
proof of Deligne's main theorem in Weil II, combining Deligne's theory of
representations of global and local monodromy groups and Laumon's use of
Deligne's $\ell$-adic Fourier transform.

Here's a tentative plan :

0. Historical sketch

1.
$\overline{\mathbf{Q}}_{\ell}$-sheaves, Grothendieck trace formula, Weil
sheaves 2. Mixed sheaves, statement of Deligne's main theorem in Weil II 3. The
global monodromy theorem, determinantal weights 4. Real sheaves and purity 5.
The weight monodromy theorem 6. The curve case implies the main theorem 7.
Review of Deligne's $\ell$-adic Fourier transform 8. Proof of the curve case

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