Fonctionne avec Indico
v3.2.9
Artin and Whaples showed it in 1945. There are two (and only two) possible « worlds » 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 « a theory of everything », 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.