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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.
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Anwesh Ray (Sat,) studied this question.
synapsesocial.com/papers/68e65993b6db6435875e887c — DOI: https://doi.org/10.48550/arxiv.2406.05524
Anwesh Ray
Chennai Mathematical Institute
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