Volume 4, Issue 6
Special volume AJAX in honor of René Schoof
Abstract:
In this article, we study the notions of order and exponent for finite flat group schemes and explore the relationship between them. A question raised by Grothendieck in SGA3 around the 1970s asks whether, as in the classical theory of finite groups, the exponent necessarily divides the order. Despite its deceptively simple formulation, this question remains mysterious and is still open in full generality. It has an illustrious history: over the past sixty years, it has attracted contributions from many mathematicians, including Grothendieck, Deligne, and Schoof, whose work yields the most general affirmative result currently known. We present the known cases, outline the main ideas on which these results are based and we present some small recent improvements.
Citation:
Emiliano Torti. Order vs exponent for finite flat group schemes. Polynesian Journal of Mathematics, Volume 4, Issue 6, Pages 1–12. (Sept. 2026) DOI: 10.69763/polyjmath.4.6
Milestones:
Received 28 Jan 2026
Revised 5 Jul 2026
Accepted 7 Jul 2026
Published 28 Sep 2026
Communicated by Samuele Anni
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