Talks
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Hilbert Class Field and Artin’s Symbol (en español) 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.
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On the problem of the rank of the Mordell-Weil group This presentation covered my research conducted during my master’s program, delivered at the CIMPA School 2025 in Valparaíso.
Seminars
Extras
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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. 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.
We thank René Schoof and Jean-Pierre Serre himself for their corrections to the project.