Key points are not available for this paper at this time.
Let Fq be the finite field with q elements, F: =Fq (T) and F^sep a separable closure of F. Set A to denote the polynomial ring FqT. Let p be a non-zero prime ideal of A, and O be the completion of A at p. Given any integer r 2, I construct a Galois representation: Gal (F^sep/F) GLᵣ (O) which is unramified at all non-zero primes l p of A, and whose image is a finite index subgroup of GLᵣ (O). Moreover, if the degree of p is 1, then is also unramified at.
Anwesh Ray (Sat,) studied this question.