Given an integer , we will first construct motivic representations (i.e., built out of pieces of the cohomology of projective smooth varieties, in fact curves)
with open image, for any which is mod and for certain . We will do this in three different ways. The third of them has a descent to when is 3 or 4. This provides us with motivic Galois representations of with open image in for any even and any which is mod 3 or mod 4.
Cite this article
Nicholas M. Katz, A note on Galois representations with big image. Enseign. Math. 65 (2019), no. 3/4, pp. 271–301DOI 10.4171/LEM/65-3/4-1