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Introduction to Rational Points on Plane Curves | 1 |
2 Factorial Properties of Polynomial Rings | 2 |
3 Pythagoras Diophantus and Fermat | 7 |
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a₁ abelian group abelian varieties algebraically closed assertion automorphism ax² b₂ bad reduction calculate change of variable Chapter characteristic coefficients cohomology complex multiplication complex numbers conic conjecture cubic curve cubic equation cyclic Definition denote discriminant divisors E(Q)tors elements elliptic curve elliptic curve defined elliptic function equation y² equivalent Euler product exact sequence factor Fermat formula Gal(K/K Galois extension Galois group given group law H¹(G Hence homogeneous homomorphism integer intersection points irreducible isogeny isomorphism j-invariant L-function Math modular modulo morphism nonsingular nonzero normal form notations number field p-adic P₁ P₂ plane curve point of order polynomial prime projective space PROOF proves the proposition proves the theorem quadratic quotient rational numbers rational points relation Remark ring roots Serre singular subgroup supersingular tangent line Tate valuation Weierstrass equation zero zeta function