A RESULT ON MODULAR FORMS IN CHARACTERISTIC p
نویسنده
چکیده
d The action of the derivation e = q ~ on the q-expansions of modular forms in characteristic p is one of the fundamental tools in the Serre/Swinnerton-Dyer theory of mod p modular forms. In this note, we extend the basic results about this action, already known for P > 5 and level one, to arbitrary p and arbitrary prime-to-p level. !. Review of modular forms in characteristic p We fix an algebraically closed field K of characteristic p > 0, an integer N > 3 prime to p, and a primitive N'th root of unity ~ ~ K. The moduli problem "elliptic curves E over N structure ~ of determinant {" is K-algebras with level represented by
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