Notes

Personal documents for general use

Transcriptions

• J.-P. Serre. Abelian $\ell$-adic representations and elliptic curves
  This book, published originally in 1989 by Addison-Wesley, is a classic one with 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 Rocío Sepúlveda Manzo 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 .

Others

Las conjeturas de Weil, cohomología étale y conjeturas de Tate (48 pp.). This was my “little thesis” as an undergraduate student with professor Héctor Pastén. Aside from folkloric results that are better exposed in Bjorn Poonen’s Rational Points on Varieties,¹ I also included some tiny original material, such as a new proof of a weak version of the Lang-Weil bounds and a remark on how Campana-Peternell’s classification of certain varieties implies that Tate’s conjectures $T^1$ hold on (sufficiently nice) varieties of dimension $\le 3$ and nef tangent bundle.

The original material was translated into English for the convenience of the reader.

The remaining notes are kept in the version of their original language. English has few ones, since most material is already covered in better expositions than mine.