Tuesdays 12.00 - 1.00 pm, Frank Adams 1
| 1 Oct | Martin | Introductory talk | |
| 8 Oct | William | Hodge structures, example of abelian varieties
Edixhoven 2, 2.1 Roughly the same material as: part of Daw 5 and 6, or Moonen 1.1, 1.6 Deligne 1.1.3-1.1.4 |
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| 15 Oct | Miriam | Algebraic groups, Deligne torus
Edixhoven 2.2, 4.1, 4.10, Milne SVI sec. 1 "Cartan involutions" Reductive groups defined via Cartan involutions (Milne SVI 1.16) Deligne 1.1.1, 1.1.15 and paragraph before it |
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| 22 Oct | Bijay | Deligne torus (recap), polarisations, Mumford-Tate groups
Daw 4, rest of 5, Edixhoven 2.5-2.7, 5.1, 5.7 Note that the proofs of Edixhoven 5.7 (not the one in the first sentence) and Milne SVI 1.20 are essentially the same. Deligne 1.1.10 | |
| 29 Oct | Bijay | Examples of Mumford-Tate groups, variations of Hodge structures
Moonen 5.2, 5.4, Milne SVI sec. 2 "Variations of hodge structures" (first 5 paragraphs), maybe some of Edixhoven 6 VHS part is roughly the same material as Edixhoven 2.8 Deligne 1.1.7-1.1.9 |
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| 5 Nov | Open plan group meeting | ||
| 12 Nov | Andrew | Axioms for Shimura data
Edixhoven 6, 6.1 (not proof), 6.2, 7.1, maybe some of 7.2-7.3 Similar material to Daw 10, Milne SVI 2.14, 5.5-5.7 Deligne 1.1.14, 1.1.18??, 2.1.1 |
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| 19 Nov | Bijay | Hermitian symmetric domains
Edixhoven 6.4, 6.5 (very brief), Daw 2, 3, Milne SVM p. 10-12 Deligne 0.4, some of 1.2 |
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| 26 Nov | Open plan group meeting | ||
| 3 Dec | Vahagn | Arithmetic, congruence, neat subgroups
Edixhoven 7.8, 7.10, Daw 11, 13, Milne SVM 3 |
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| 10 Dec | Guy | Definition of Shimura variety components/locally symmetric varieties, Baily-Borel
Orr-Skorobogatov 3.1, Edixhoven 7.14, Daw 15, 16, Milne SVM 4 (more details in Milne SVI 3) |
Daw: André-Oort via o-minimality
Deligne: Variétés de Shimura (English translation by Milne)
Edixhoven: Shimura varieties, notes for some introductory lectures
Kerr: Shimura varieties: A Hodge-theoretic perspective
Milne SVI: Introduction to Shimura varieties
Milne SVM: Shimura varieties and moduli
Moonen: An introduction to Mumford-Tate groups
Orr-Skorobogatov: Finiteness theorems for K3 surfaces and abelian varieties of CM type