• Every BT1 group scheme appears in a Jacobian

      Pries, Rachel; Ulmer, Douglas; Department of Mathematics, University of Arizona (American Mathematical Society (AMS), 2021-11-04)
      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. Our main result is that every BT1 group scheme over k occurs as a direct factor of the p-torsion group scheme of the Jacobian of an explicit curve defined over Fp. We also treat a variant with polarizations. Our main tools are the Kraft classification of BT1 group schemes, a theorem of Oda, and a combinatorial description of the de Rham cohomology of Fermat curves.