Reduction of the Manin map modulo $p$

Details Reduction of the Manin map modulo $p$ Reduction of the Manin map modulo $p$

1994-07-13

arxiv.org/abs/alg-geom/9407006v1

Mathematics

Algebraic Geometry

11 pages, LaTeX

Scientific paper

For an abelian variety $A$ over a function field $K$ of characteristic zero, Manin defined a remarkable additive map $A(K) \ra V$, where $V$ is a vector space over $K$. We define an analogue of this map in the case of function fields of characteristic $p$. We then prove that the reduction modulo $p$ of the Manin map in characteristic zero is the derivative of the Manin map in characteristic $p$ and that the kernel of the Manin map in characteristic $p$ is the group of points divisible by $p$.

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