NERON SYMBOL ON ${\kappa}-HOLOMORPHIC$ TORUS

Abstract

S. Turner has shown that a Neron symbol can be calculated from the values of K-meromorphic theta functions corresponding to divisors on K-holomorphic torus of strongly diagonal type. Using an isogeny to a K-holomorphic torus of strongly diagonal type, he constructed a Neron symbol on K-holomorphic torus of diagonal type. In this work, we provide a simple formula of the Neron symbol on the Tate curve. And then we construct the Neron symbol on K-holomorphic torus of diagonal or st rongly diagonal type without using isogenies.

Keywords

• Neron symbol;
• K-holomorphic torus of storngly diagonal type;
• diagonal type;
• theta functions

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References

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