The Eisenstein Quotient of the Jacobian Variety of a Drinfeld Modular Curve | Zendy

Akio Tamagawa | Zendy

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The Eisenstein Quotient of the Jacobian Variety of a Drinfeld Modular Curve

Author(s) -

Akio Tamagawa

Publication year - 1995

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195164439

Subject(s) - mathematics , quotient , jacobian matrix and determinant , pure mathematics , modular curve , ideal (ethics) , function field , variety (cybernetics) , modular form , field (mathematics) , discrete mathematics , algebra over a field , arithmetic , philosophy , statistics , epistemology

Let K = ¥q(T\ the rational function field over the finite field ¥q (T: indeterminate), and A=¥q[T]. For a non-zero ideal n of A, we can define a smooth proper geometrically connected curve X0(n) over K, called the Drinfeld modular curve of Hecke type with conductor n. In this article, we define the "Eisenstein quotient" J of the Jacobian variety / of Jf0(n) for n maximal and investigate its arithmetic properties. One of the main results is as follows :

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