This course is part of the MRI Masterclass 'Moduli spaces'. We develop the basics of complex abelian varieties and the theta functions on them. A motivating example will be jacobians of compact Riemann surfaces. Our treatment of the material will be close to the following book:

H.P.F. Swinnerton-Dyer, *Analytic theory of abelian varieties*. London Mathematical Society Lecture Note Series 14. Cambridge University Press. ISBN 0-521-20526-3.

Here one may find some further references to the literature: pdf.

Assignment I: Exercises I.2, I.3, II.7, III.3, III.5. Due October 7.

Assignment II: Exercises IV.2(i),(iii),(vii), V.1, V.4, V.5, VI.1. Due October 28 (NB: deadline extended to November 4).

Assignment III: Exercises VII.1, VII.3, VII.5, VII.6, IX.1. Due November 18.

Assignment IV: Exercises IX.3, XI.2, XI.3, XI.4, XI.6. Due December 16.

The homework grades can be found here. Note that there are some spots left open; please make sure I can fill these a.s.a.p.

Please send me an email if you wish your homework sheets to be mailed to your home address.

Written exam: Tuesday, January 25th, 14.00-17.00 in Room 611 of the Mathematics Department. Books and notes may be used; one may not use a mobile phone or an internet connection.

Exercise sheet I: pdf.

Exercise sheet II: pdf.

Exercise sheet III: pdf.

Exercise sheet IV: pdf.

Exercise sheet V: pdf.

Exercise sheet VI: pdf.

Exercise sheet VII: pdf.

Exercise sheet VIII: pdf.

Exercise sheet IX: pdf.

Exercise sheet X: take another look at the exx. up till now.

Exercise sheet XI: pdf.

Exercise sheet XII: pdf.