Talk 9: Formal Immersions and Quotients of Modular Jacobians
نویسنده
چکیده
We establish some notation. Let N be prime and set S = SpecZ[1/2N ]. Denote by XQ = X0(N)/Q and JQ = J0(N) the usual modular curve and its Jacobian over Q, where we normalize the embedding XQ →֒ JQ by requiring ∞ 7→ 0. XQ is the generic fiber of the (smooth) S-curve X = X0(N)/S , and JQ has Néron model J = NéronS(J0(N)), which is in fact an abelian scheme over S. The Néron mapping property gives us a map X → J extending the map over Q. T will denote the usual Hecke algebra, viewed (when convenient) as a subalgebra of EndQ(JQ), and we put TA = T ⊗Z A for an abelian group A. Note that T also acts on J (over S) by the Néron mapping property.
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