On BT₁ group schemes and Fermat Jacobians

2020/10/28 by Rachel Pries, Pries, Rachel, Douglas Ulmer +1
Mathematics · Medicine · #11D41 #11G20 #14F40 #14G17 #14H10 #14H40 #14K15 #14L05 (Secondary) #14L15 (Primary) 11G10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Leprosy Research and Treatment #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2010.15160

openalex publication_date 2020/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number and let k be an algebraically closed field of characteristic p. A BT₁ group scheme over k is a finite commutative group scheme which arises as the kernel of p on a p-divisible (Barsotti--Tate) group. We compare three classifications of BT₁ group schemes, due in large part to Kraft, Ekedahl, and Oort, and defined using words, canonical filtrations, and permutations. Using this comparison, we determine the Ekedahl--Oort types of Fermat quotient curves and we compute four invariants of the p-torsion group schemes of these curves.

Citations

• The p-rank of Artin-Schreier curves
• The Dieudonné modules and Ekedahl-Oort types of Jacobians of hyperelliptic curves in odd characteristic
• Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties

Related

• Every BT₁ group scheme appears in a Jacobian
• The Dieudonné modules and Ekedahl-Oort types of Jacobians of hyperelliptic curves in odd characteristic
• Computing discrete invariants of varieties in positive characteristic. I. Ekedahl-Oort types of curves
• The Ekedahl-Oort type of Jacobians of Hermitian curves
• Class field theory for function fields and finite abelian torsors