Algebraic geometry: arithmetic techniques
Michael Groechenig 
Notes:  Lecture Notes 
Literature: 
Popa's lecture notes 
Essay topics: 
List of topics 
Problems: 
Problem sheet 1 
Problem sheet 2 

Problem sheet 3 

Problem sheet 4 

Problem sheet 5 

Problem sheet 6 

Problem sheet 7 

Problem sheet 8 

There's no problem sheet 9 so you can work on the essay. 

Problem sheet 10 

Problem sheet 11 