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searching for Shafarevich conjecture 8 found (9 total)

Tate–Shafarevich group (1,381 words) [view diff] exact match in snippet view article find links to article

abelian variety is closely related to the Selmer group. The Tate–Shafarevich conjecture states that the Tate–Shafarevich group is finite. Karl Rubin proved

Eric Urban (379 words) [view diff] exact match in snippet view article find links to article

Gross-Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich conjecture) of the conjecture that E has infinitely many rational points if

Gerd Faltings (507 words) [view diff] exact match in snippet view article find links to article

the Tate conjecture for abelian varieties over number fields, the Shafarevich conjecture for abelian varieties over number fields and the Mordell conjecture

Christopher Skinner (515 words) [view diff] exact match in snippet view article find links to article

Gross–Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich conjecture) of the conjecture that E has infinitely many rational points if

Main conjecture of Iwasawa theory (1,108 words) [view diff] exact match in snippet view article find links to article

Gross-Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich conjecture) of the conjecture that E has infinitely many rational points if

Aleksei Parshin (1,323 words) [view diff] exact match in snippet view article find links to article

arXiv:math/0004078. Heier, Gordon (2003). "Uniformly effective Shafarevich conjecture on families of hyperbolic curves over a curve with prescribed degeneracy

Igor Shafarevich (2,466 words) [view diff] exact match in snippet view article find links to article

version of the Torelli theorem for K3 surfaces. He formulated the Shafarevich conjecture, which stated the finiteness of the set of Abelian varieties over

List of conjectures (1,517 words) [view diff] exact match in snippet view article find links to article

Faltings Mordell conjecture number theory ⇐Faltings's theorem, the Shafarevich conjecture on finiteness of isomorphism classes of abelian varieties. The reduction