Séminaire des Doctorants et Doctorantes - Institut Camille Jordan - ICJ - Villeurbanne - Sud-Est - Unité de mathématiques pures et appliquées - UMPA/ENSL - Lyon - Sud-Est

Institut Camille Jordan - ICJ - Villeurbanne - Sud-Est Unité de mathématiques pures et appliquées - UMPA/ENSL - Lyon - Sud-Est

Arithmetic in the "Upside Down"

Speaker: Gazda, Quentin ()
Title: Arithmetic in the "Upside Down"
Abstract: <p>Artin and Whaples showed it in 1945. There are two (and only two) possible «&nbsp;worlds&nbsp;» in which one can do arithmetic. One is much more present in our daily life: it is the usual number theory over number fields (finite field extensions of $\mathbb{Q}$). But on the other side of the mirror, there is the arithmetic over function fields in positive characteristic. Most of the known theorems and conjectures in number theory have a counter part in function fields arithmetic, and the former statements are in general easier to prove in the function fields case. It is believed that «&nbsp;a theory of everything&nbsp;», mixing and understanding both worlds at once, would have outstanding consequences in arithmetic. My talk will be devoted to the introduction of function fields arithmetic.</p>

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ref: Séminaire des Doctorants et Doctorantes - Institut Camille Jordan - ICJ - Villeurbanne - Sud-Est - Unité de mathématiques pures et appliquées - UMPA/ENSL - Lyon - Sud-Est