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Rank of Elliptic Curves over almost Separably Closed Fields
Author(s) -
Larsen Michael
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002431
Subject(s) - mathematics , separable space , rank (graph theory) , elliptic curve , closure (psychology) , invariant (physics) , pure mathematics , supersingular elliptic curve , schoof's algorithm , combinatorics , mathematical analysis , quarter period , mathematical physics , economics , market economy
Let E be an elliptic curve over a finitely generated infinite field K . Let K s denote a separable closure of K , σ an element of the Galois group G K =Gal( K s / K ), and K s (σ) the invariant subfield of K s . If the characteristic of K is not 2 and σ belongs to a suitable open subgroup of G K , then E ( K s (σ)) has infinite rank. 2000 Mathematics Subject Classification 11G05.