Frey Curve
المؤلف:
Cox, D. A.
المصدر:
"Introduction to Fermat,s Last Theorem." Amer. Math. Monthly 101
الجزء والصفحة:
...
8-7-2020
1388
Frey Curve
Let 
be a solution to Fermat's last theorem. Then the corresponding Frey curve is
 |
(1)
|
Ribet (1990a) showed that such curves cannot be modular, so if the Taniyama-Shimura conjecture were true, Frey curves couldn't exist and Fermat's last theorem would follow with 
even and 
. Frey curves are semistable. Invariants include the elliptic discriminant
 |
(2)
|
The minimal discriminant is
 |
(3)
|
the j-conductor is
 |
(4)
|
and the j-invariant is
 |
(5)
|
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.
Ribet, K. A. "From the Taniyama-Shimura Conjecture to Fermat's Last Theorem." Ann. Fac. Sci. Toulouse Math. 11, 116-139, 1990a.
Ribet, K. A. "On Modular Representations of 
Arising from Modular Forms." Invent. Math. 100, 431-476, 1990b.
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