Seminar "Topics in Algebraic Geometry"
In the Spring Semester of 2012, we (Michiel Kosters and Bas Edixhoven) are organizing a seminar "Topics in Algebraic Geometry". The seminar will take place on Mondays, just before the Algebra, geometry and number theory seminar. We especially encourage people who followed Advanced Algebraic Geometry to participate.
We start by studying parts of the book "Arithmetic Moduli of Elliptic Curves" of Katz and Mazur. This leads naturally to modular curves, modular forms, group schemes, deformation theory. We might study other subjects which are of interest for the participants.
If you want to participate, have any suggestions or comments, or if you want to give a talk, please send an email to Michiel Kosters.
Students can get credit points for active participation.
Schedule
Lectures will take place in Room 174 (6-2-2012), 312 (13-2-2012 - 23-3-2012) and 404 (30-3-2012--) on Mondays from 13:45-15:45 (at least till 30-4-2012).
February 6, 2012. Room 174.
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13:45h-14:45h. Bas Edixhoven. Introduction
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14:45h-15:45h. Michiel Kosters. Effective Cartier divisors (1.1) Notes
February 13, 2012. Room 312.
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13:45h-15:45h. Rene Pannekoek. The group law on elliptic curves over an arbitrary base scheme I (2.1)
February 27, 2012. Room 312.
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13:45h-15:45h. Rene Pannekoek. The group law on elliptic curves over an arbitrary base scheme II (2.1)
March 5, 2012. Room 312.
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13:45-15:45h. Jinbi Jin. Differentials and translation actions on modules on group schemes Notes
March 12, 2012. Room 312.
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13:45-15:45h. Jinbi Jin. Generalised Weierstrass equations and elementary universal families Notes
March 19, 2012. 312.
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13:45-15:45h. Johan Commelin. The structure of [N] Notes
March 26, 2012. 312.
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13:45-x. Johan Commelin. The structure of [N] Notes
x-15:45h. Maarten Derickx. Representability of some moduli problems. Notes
April 2, 2012. 312.
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13.45:15.45h. Maarten Derickx. Representability of some moduli problems. Notes
April 16, 2012. 312.
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13.45:15.45h. Maxim Mornev Tate curve. Reference
April 23, 2012. 312.
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13.45:15.45h. Maxim Mornev Tate curve. Reference
May 7, 2012. 312.
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13.45:15.45h. Pietro Mercuri. Isogenies, duality and Frobenius. Notes
May 14, 2012. 312.
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13.45:15.45h. Bas Edixhoven. Katz modular forms. Notes
May 21, 2012. 312.
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13.45:15.45h. Milan Lopuhaa. Coarse moduli schemes and the j-line.
Bibliography
- Katz and Mazur Arithmetic Moduli of Elliptic Curves (Download)
If you think other references are useful, please tell us.
Participants
- (Samuele Anni)
- (Raymond van Bommel)
- Johan Commelin
- Maarten Derickx
- Bas Edixhoven
- Alberto Gioia
- Johannes Petrus van der Horst
- Sean Howe
- Robin de Jong
- Jinbi Jin
- Michiel Kosters
- Milan Lopuhaa
- Pietro Mercuri
- Maxim Mornev
- Rene Pannekoek
- Andrea Siviero
- Lenny Taelman
- (Wouter Zomervrucht)
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