AffiliationDepartment of Mathematics, University of Arizona
De Rham cohomology
MetadataShow full item record
PublisherAmerican Mathematical Society (AMS)
CitationPries, R., & Ulmer, D. (2022). Every BT1 Group Scheme Appears in a Jacobian. Proceedings of the American Mathematical Society, 150(2), 525–537.
Rights© 2021 American Mathematical Society.
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AbstractLet 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.
VersionFinal accepted manuscript
SponsorsNational Science Foundation