This research extends results on simple group schemes for primes ≤ 37, implying deeper insights into finite flat group structures.
Since simple commutative finite flat group schemes G over Z are killed by a prime number p, their order is a power of p. Tate asked whether a simple group scheme G is necessarily equal to Z/pZ or μ p . This has been proved for primes p≤19. Under assumption of the Generalized Riemann Hypothesis we extend this result to primes p≤37.
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Dembélé et al. (2025) studied this question.
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