Talks

• Hilbert Class Field and Artin’s Symbol This lecture was part of the seminar on Explicit Class Field Theory taught in the first semester at PUC. It introduces the concepts of place, ramification, Hilbert class fields, and the Artin symbol.

Seminars

• Seminar on Galois representations and their $L$-functions

Extras

• Undergraduate’s thesis

• J.-P. Serre. Abelian $\ell$-adic representations and elliptic curves
  This book, published originally in 1989 by Addison-Wesley, is a classic onewith two main issues for future diffusion: the first being that it is out of print; and the second being that it is written in typewriter machine, which can be aesthetically repulsive to certain readers. The need for this book is that modern texts on elliptic curves or abelian varieties don’t go deep enough on the subject (including Silverman’s Advanced topics…), while it is still acknowledged as obligatory for investigation purposes.

  Alongside José Cuevas we decided to perform the project of re-typing it in modern LaTeX, while still maintaining most of the original style. The project is still ongoing, but you can download the temporary pdf file here