Arithmetic from an advanced perspective: an introduction to the Adeles
Palabras clave:
Adele ring, nonarchimedean analysis, p-adic numbers
Resumen
Here we offer an introduction to the adele ring over the field of rational numbers Q and highlight some of its beautiful algebraic and topological structure. We then apply this rich structure to revisit some ancient results of number theory and place them within this modern context as well as make some new observations. We conclude by indicating how this theory enables us to extend the basic arithmetic of Q to the more subtle, complicated, and interesting setting of an arbitrary number field.
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Cómo citar
Burger, E. (2010). Arithmetic from an advanced perspective: an introduction to the Adeles. Pro Mathematica, 24(47-48), 149-195. Recuperado a partir de https://revistas.pucp.edu.pe/index.php/promathematica/article/view/10278
Derechos de autor 2016 Pro Mathematica
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.