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|23.10.2024 | |23.10.2024 | ||
| | |Hodge-Tate decomposition for p-divisible groups : The universal vector extension./ | ||
Cover [Tam06], 1.2 on vector groups, section 1.4 on the universal vector extension of a p-divisible group and finally section 2.3 on the module ωE. | |||
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|3 | |3 | ||
|30.10.2024 | |30.10.2024 | ||
| | |Hodge-Tate decomposition for p-divisible groups : The period pairing and Hodge-Tate decomposition. | ||
Introduce the ring A1 inf following [Tam06], 2.1. Define the period pairing following section 3.1. Finally deduce the Hodge-Tate decomposition in section 3.2. | |||
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|4 | |4 | ||
|06.11.2024 | |06.11.2024 | ||
| | |Crystalline cohomology : Divided power structures. / | ||
Discuss some basic algebraic preliminaries on divided powers, following [BO78], §3. More precisely cover 3.1 – 3.5, explain Theorem 3.9 about the divided power algebra without proof, explain extensions and compatible PD-structures 3.14 – 3.17. Discuss PD-envelopes in 3.19. Only sketch the construction if time permits. Cover 3.21 – 3.22, Definitions 3.24 and 3.29, Finally, briefly discuss how to globalize to schemes. | |||
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|5 | |5 | ||
|13.11.2024 | |13.11.2024 | ||
| | |Crystalline cohomology : Crystalline cohomology. / | ||
Introduce the crystalline site and topos following [BO78], §5 until Example 5.2. Briefly sketch the construction of g∗ crys and gcrys,∗ given in 5.6 – 5.8 and state Proposition 5.9. Define global sections and crystalline cohomology in Definition 5.15 and the discussion following it. Define the morphisms of topoi uX/S and iX/S relating the crystalline and Zariski topos. Show Propositions 5.25 – 5.27. Minimize the amount of the categorical nonsense before that. | |||
|TBA | |TBA | ||
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Revision as of 10:28, 8 October 2024
Winter Semester 24/25
Oberseminar - Explicit reciprocity laws and applications.
Time and place: Wednesday 10-12, SFB Lecture Hall (M311). [ Explicit reciprocity laws and applications programme will come in september ]
| No | Date | Title / Abstract | Speaker |
|---|---|---|---|
| 1 | 16.10.2024 | Hodge-Tate decomposition for p-divisible groups : p-divisible groups./
Briefly discuss the (co)tangent space and differentials for affine group schemes following [Tam06], 1.1. Define p-divisible groups following loc. cit., 1.3. Discuss section 2.2. Finally explain the relation between p-divisible groups and formal groups by explaining [Mor16], Proposition 4.12. For time reasons, you may focus on how to obtain a p-divisible group from a formal group. |
tba |
| 2 | 23.10.2024 | Hodge-Tate decomposition for p-divisible groups : The universal vector extension./
Cover [Tam06], 1.2 on vector groups, section 1.4 on the universal vector extension of a p-divisible group and finally section 2.3 on the module ωE. |
tba |
| 3 | 30.10.2024 | Hodge-Tate decomposition for p-divisible groups : The period pairing and Hodge-Tate decomposition.
Introduce the ring A1 inf following [Tam06], 2.1. Define the period pairing following section 3.1. Finally deduce the Hodge-Tate decomposition in section 3.2. |
tba |
| 4 | 06.11.2024 | Crystalline cohomology : Divided power structures. /
Discuss some basic algebraic preliminaries on divided powers, following [BO78], §3. More precisely cover 3.1 – 3.5, explain Theorem 3.9 about the divided power algebra without proof, explain extensions and compatible PD-structures 3.14 – 3.17. Discuss PD-envelopes in 3.19. Only sketch the construction if time permits. Cover 3.21 – 3.22, Definitions 3.24 and 3.29, Finally, briefly discuss how to globalize to schemes. |
tba |
| 5 | 13.11.2024 | Crystalline cohomology : Crystalline cohomology. /
Introduce the crystalline site and topos following [BO78], §5 until Example 5.2. Briefly sketch the construction of g∗ crys and gcrys,∗ given in 5.6 – 5.8 and state Proposition 5.9. Define global sections and crystalline cohomology in Definition 5.15 and the discussion following it. Define the morphisms of topoi uX/S and iX/S relating the crystalline and Zariski topos. Show Propositions 5.25 – 5.27. Minimize the amount of the categorical nonsense before that. |
TBA |
| 6 | 20.11.2024 | tba | tba |
| 7 | 27.11.2024 | tba | tba |
| 8 | 04.12.2024 | tba | tba |
| 9 | 11.12.2024 | tba | tba |
| 10 | 18.12.2024 | tba | tba |
| 11 | 15.01.2025 | tba | TBA |
| 12 | 22.01.2025 | ||
| 13 | 29.01.2025 | ||
| 14 | 05.02.2025 |
Winter Semester 23/24
Oberseminar - Euler systems
Time and place: Thursday 10-12, SFB Lecture Hall. Programme
| No | Date | Title / Abstract | Speaker |
|---|---|---|---|
| 1 | 19.10.2023 | Euler systems and main results. | Zhenghang Du |
| 2 | 26.10.2023 | Euler systems and main results. | Zhenghang Du |
| 3 | 02.11.2023 | Example: cyclotomic units. | Chiara Sabadin |
| 4 | 09.11.2023 | Example: elliptic curves with CM I. | Christoph Fronhöfer |
| 5 | 16.11.2023 | Example: elliptic curves with CM II. | TBA |
| 6 | 23.11.2023 | The derivative construction. | Julio de Mello Bezerra |
| 7 | 30.11.2023 | Local properties of derivative classes. | Guido Kings |
| 8 | 07.12.2023 | Bounding the order of the Selmer group. | Lukas Prader |
| 9 | 14.12.2023 | Twisting of Euler systems. | Han-Ung Kufner |
| 10 | 21.12.2023 | Iwasawa theory I. | Bence Forrás |
| 11 | 11.01.2024 | Iwasawa theory II. | TBA |
| 12 | 18.01.2024 | ||
| 13 | 25.01.2024 | ||
| 14 | 01.02.2024 |
Summer Semester 23
Oberseminar - Modular Galois representations
Time and place: Thursday 10-12, SFB Lecture Hall.
| No | Date | Title / Abstract | Speaker |
|---|---|---|---|
| 1 | 20.04.2023 | Group representations and semi-simple algebras | Chiara Sabadin |
| 2 | 27.04.2023 | Group representations and semi-simple algebras | Chiara Sabadin |
| 3 | 04.05.2023 | Representations and pseudo-representations with coefficients in Artin rings | Guillermo Gamarra-Segovia |
| 4 | 11.05.2023 | Representations and pseudo-representations with coefficients in Artin rings | Guillermo Gamarra-Segovia |
| 5 | 18.05.2023 | holiday | |
| 6 | 25.05.2023 | Deformation of group representations | Zhenghang Du |
| 7 | 01.06.2023 | Deformation of group representations | Zhenghang Du |
| 8 | 08.06.2023 | holiday | |
| 9 | 15.06.2023 | The q-expansion principle and p-adic Hecke algebras | Julio de Mello Bezerra |
| 10 | 22.06.2023 | The q-expansion principle and p-adic Hecke algebras | Julio de Mello Bezerra |
| 11 | 29.06.2023 | no meeting due to Oberwolfach | |
| 12 | 06.07.2023 | Modular Galois representations | Lukas Prader |
| 13 | 13.07.2023 | Taylor-Wiles systems for the Hecke algebra | Guido Kings |
| 14 | 20.07.2023 | Universal deformation rings and Taylor-Wiles systems | Han-Ung Kufner |
Winter Semester 22/23
AG Seminar - Main conjecture for totally real fields
| No | Date | Title / Abstract | Speaker |
|---|---|---|---|
| 1 | 19.10.2022 | The p-adic L-function and the main conjecture | Julio de Mello Bezerra |
| 2 | 26.10.2022 | The p-adic L-function and the main conjecture (continuation) | Julio de Mello Bezerra |
| 3 | 02.11.2022 | \Lambda-adic modular forms | Guillermo Gamarra-Segovia |
| 4 | 09.11.2022 | \Lambda-adic modular forms (continuation) | Guillermo Gamarra-Segovia |
| 5 | 16.11.2022 | \Lambda-adic Eisenstein series | Lukas Prader |
| 6 | 23.11.2022 | \Lambda-adic Eisenstein series (continuation) | Lukas Prader |
| 7 | 30.11.2022 | \Lambda-adic cusp forms | Zhenghang Du |
| 8 | 07.12.2022 | Galois representations associated to \Lambda-adic forms | Chiara Sabadin |
| 9 | 14.12.2022 | Galois representations associated to \Lambda-adic forms (continuation) | Chiara Sabadin |
| 10 | 21.12.2022 | The Eisenstein ideal and stable lattices | Han-Ung Kufner |
| 11 | 11.01.2023 | The Eisenstein ideal and stable lattices (continuation) | Han-Ung Kufner |
| 12 | 18.01.2023 | The Eisenstein ideal and stable lattices (continuation) | Han-Ung Kufner |
| 13 | 01.02.2023 | The Galois representation of a stable lattice | Johannes Sprang |
| 14 |
