“Frey Curve”的概念、定义、习题解题方法及翻译-数学辞典

单词

Frey Curve

释义

Frey Curve

Let be a solution to Fermat's Last Theorem. Then the corresponding Frey curve is

(1)

Frey showed that such curves cannot be Modular, so if the Taniyama-Shimura Conjecturewere true, Frey curves couldn't exist and Fermat's Last Theorem would follow with

Even and

.Frey curves are Semistable. Invariants include the Discriminant

(2)

The Minimal Discriminant is

(3)

the Conductor is

(4)

and the j-Invariant is

(5)

See also Elliptic Curve, Fermat's Last Theorem, Taniyama-Shimura Conjecture

References

Cox, D. A. ``Introduction to Fermat's Last Theorem.'' Amer. Math. Monthly 101, 3-14, 1994.

Gouvêa, F. Q. ``A Marvelous Proof.'' Amer. Math. Monthly 101, 203-222, 1994.

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