Restriction of sections of abelian schemes

Najmuddin Fakhruddin

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arXiv · math/0310405

Restriction of sections of abelian schemes

Najmuddin Fakhruddin

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Abstract

We prove the following result: Let B be a smooth, irreducible, quasi-projective variety over the complex numbers and assume that B has a projective compactification \bar{B} such that \bar{B} - B is of codimension at least two in \bar{B}. Then there exists a family of smooth ireducible curves {C_q}_{q \in Q} in B parametrised by an irreducible variety Q such that if p: A \to B is an abelian scheme and q \in Q is a generic point, then the restriction map on sections A(B) \to A(C_q) is an isomorphism. This answers, in a special case, a question of Graber, Harris, Mazur and Starr.

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BibTeX RIS

Najmuddin Fakhruddin. 2003-10-25. Restriction of sections of abelian schemes. https://arxiv.org/abs/math/0310405

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