Motives and the inverse Galois problem
Zhiwei Yun, MIT

We will use geometric Langlands theory to solve two problems simultaneously. One is Serre's question that whether there exist motives over Q with motivic Galois groups of type E_8 or G_2; the other is whether there are Galois extensions of Q with Galois groups E_8(p) or G_2(p) (the finite simple groups of Lie type). The answers to both questions are YES. No knowledge of motives or Langlands will be assumed.

Motives and the inverse Galois problem Zhiwei Yun, MIT

Motives and the inverse Galois problem
Zhiwei Yun, MIT