Course work topics

Satoshi Kondo

1st-2nd year.  
p-adic numbers, Hensel's lemma
References: 
Coppel "Number Theory" (Universitext), 
Cassels "Local Fields" (Cambridge), 
Gouvea "p-adic numbers: an introduction" (Universitext).
Fesenko-Vostokov "Local Fields and Their Extensions" Chapters 1, 2
https://www.maths.nottingham.ac.uk/personal/ibf/book/book.html

1st-2nd year.  
finite fields, function fields, congruence zeta, Weil's theorem, the Weil conjecture.  
Reference:  
Koblitz "p-adic numbers, p-adic anaysis and zeta functions" Ch.5.  
There are other references.

2nd-3rd year.  
algebraic K-theory upto Milnor:  K_0 K_1 K_2 of rings,  Milnor K-theory
References: 
Weibel "The Kbook: an introduction to algebraic K-theory",
Milnor "An introduction to algebraic K-theory".
Fesenko-Vostokov "Local Fields and Their Extensions" Chapter 9
https://www.maths.nottingham.ac.uk/personal/ibf/book/book.html

Seminars and the course work will be in English.
I first ask you to solve the exercise problems in the references above.