THE MODULARITY THEOREM AND FERMAT'S LAST THEOREM
Fermat’s Last Theorem (FLT) is one of the most important and challenging problems of the last centuries in Number Theory. Its complete proof rest on the Modularity Conjecture for semistable elliptic curve defined over Q, proven to be true only in 1994 by A. Wiles.
The seminar will give an introduction to FLT, focusing on some historical aspects of its proof. In the second part we will give to the audience the statement of the Modularity theorem and introduce in an elementary way the arithmetic objects involved in it. We intend moreover to give a brief account of the implication Modularity -> FLT.