Statements (48)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical group
|
| gptkbp:can_be |
finite or infinite
|
| gptkbp:defines |
Mordell-Weil_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Tate-Shafarevich group
|
| gptkbp:is |
important for understanding the arithmetic of elliptic curves
an object that can be studied using the theory of motives related to the study of rational points on elliptic curves an object that can be computed using descent theory a group that can be analyzed using cohomological methods a finite group under certain conditions a group that can be computed in some cases a group that can be computed in specific cases a key concept in modern number theory an important concept in arithmetic geometry an important concept in the theory of motives an object of research in algebraic number theory an object of research in modern number theory associated with the study of abelian varieties connected to the study of L-functions related to the study of the arithmetic of elliptic curves related to Galois cohomology related to the concept of local fields related to the rank of an elliptic curve related to the study of Galois representations studied in the context of modular forms used in the study of rational points on varieties an important concept in the study of rational points an object of study in the context of arithmetic geometry a group that can be finite or infinite depending on the context a group that can be finite under certain conditions an object of interest in the study of arithmetic geometry related to the study of the arithmetic of abelian varieties an object of interest in arithmetic algebraic geometry an important concept in the study of L-functions and elliptic curves a group that can be analyzed using the theory of heights and descent. related to the study of rational points on algebraic varieties a group that can be analyzed using the theory of heights a_central_object_in_the_Birch_and_Swinnerton-Dyer_conjecture an_important_concept_in_the_study_of_Diophantine_equations a_subject_of_interest_in_the_Langlands_program associated_with_the_Selmer_group |
| gptkbp:measures |
failure_of_the_Hasse_principle
|
| gptkbp:namedAfter |
gptkb:Igor_Shafarevich
gptkb:John_Tate |
| gptkbp:relatedTo |
Number theory
Elliptic curves Algebraic_geometry |
| gptkbp:symbolizes |
Sha
|