Statements (115)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:musical_group
|
| gptkbp:applies_to |
Number theory
|
| gptkbp:associated_with |
Mordell-Weil theorem
Selmer group |
| gptkbp:can_be_computed_for |
Specific elliptic curves
|
| gptkbp:describes |
Obstruction to the Hasse principle
|
| gptkbp:element |
Elliptic curve theory
|
| gptkbp:has_applications_in |
gptkb:crypt
|
| gptkbp:has_connection_to |
Abstract algebra
Mathematical frameworks |
| https://www.w3.org/2000/01/rdf-schema#label |
Tate-Shafarevich group
|
| gptkbp:is_a |
Group theory
|
| gptkbp:is_afield_of_inquiry_in |
gptkb:Mathematics
|
| gptkbp:is_an_important_concept_in |
Modern number theory
|
| gptkbp:is_analyzed_in |
gptkb:Modular_forms
Research papers Algebraic topology Algebraic geometers |
| gptkbp:is_aresearch_area_in |
Number theory
|
| gptkbp:is_aresearch_topic_in |
gptkb:Mathematics
|
| gptkbp:is_associated_with |
Mathematical models
Rational points on curves |
| gptkbp:is_connected_to |
gptkb:Elliptic_curve_cryptography
Algebraic structures Mathematical proofs Rational points Class field theory L-functions Moduli spaces Rational points on algebraic varieties Mathematical conjectures Elliptic curve theory advancements Heights on varieties Rational points on elliptic curves |
| gptkbp:is_considered |
Homological algebra
Arithmetic of elliptic curves |
| gptkbp:is_defined_by |
Elliptic curves over number fields
|
| gptkbp:is_discussed_in |
Academic journals
Mathematical literature Mathematical conferences Mathematical seminars Mathematical textbooks |
| gptkbp:is_examined_in |
Mathematical analysis
Research papers Mathematicians Graduate studies Mathematical research papers Advanced mathematics courses Theoretical physicists Number theory research Arithmetic of elliptic curves |
| gptkbp:is_explored_in |
Theoretical mathematics
Mathematical literature Mathematical journals Mathematical frameworks Geometric Langlands program |
| gptkbp:is_influenced_by |
Algebraic topology
Historical mathematics |
| gptkbp:is_influential_in |
Research methodologies
Modern mathematics Theoretical mathematics Mathematical research |
| gptkbp:is_involved_in |
gptkb:Birch_and_Swinnerton-Dyer_conjecture
Class field theory Arithmetic geometry research |
| gptkbp:is_noted_for |
Theoretical implications
Conjectural properties Conjecture on finiteness |
| gptkbp:is_part_of |
gptkb:Elliptic_curve_cryptography
gptkb:Algebraic_number_theory Algebraic geometry Mordell-Weil theorem Mathematical theories Elliptic curve theory The study of algebraic structures The study of elliptic curves Theoretical explorations in mathematics Theoretical frameworks in mathematics |
| gptkbp:is_related_to |
gptkb:Arithmetic_functions
gptkb:Birch_and_Swinnerton-Dyer_conjecture gptkb:Modular_forms Rational points Galois cohomology Galois representations L-functions Cohomology theories Arithmetic geometry research Elliptic curve isogenies |
| gptkbp:is_studied_for |
Rational points on varieties
|
| gptkbp:is_studied_in |
gptkb:Algebraic_number_theory
gptkb:Mathematics Algebraic geometry Mathematical analysis Mathematicians Number theorists Graduate students Advanced mathematics courses Theoretical mathematicians |
| gptkbp:is_used_in |
gptkb:crypt
Arithmetic geometry Theoretical explorations The study of Diophantine equations |
| gptkbp:is_utilized_in |
gptkb:Data_Analytics
Computational mathematics Mathematical research |
| gptkbp:named_after |
gptkb:Igor_Shafarevich
gptkb:John_Tate |
| gptkbp:related_to |
gptkb:Elliptic_curves
Number theory Galois cohomology Selmer group |
| gptkbp:used_in |
Arithmetic geometry
|
| gptkbp:was_akey_figure_in |
Elliptic curve theory
|
| gptkbp:bfsParent |
gptkb:Birch_and_Swinnerton-Dyer_Conjecture
|
| gptkbp:bfsLayer |
7
|