Finite flat $p$-group schemes over $\mathbf{Z}$

Abstract: Conjecture (Abrashkin-Fontaine): For $p$ prime, the only simple finite flat group schemes of $p$-power order defined over $\mathbf{Z}$ are $\mathbf{Z}/p\mathbf{Z}$ and $\mu_p$.

Abrashkin and Fontaine separately proved that this conjecture is true for $p \le 17$. In this talk, we extend their result to the primes $p \le 37$ under GRH. (This is joint work with René Schoof.)

number theory

Audience: researchers in the discipline

London number theory seminar

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