Last modified date: <%+ tp.file.last_modified_date() %>
- Tags:
- Refs:
- Links:
Mordell-Lang conjecture
The Mordell-Lang #open/conjectures Let \(X\) be a closed geometrically integral subvariety of a semiabelian variety \(A\) defined over a field \(K\) of characteristic 0 . Let \(\Gamma\) be a finitely generated subgroup of \(A(\mkern 1.5mu\overline{\mkern-1.5muK\mkern-1.5mu}\mkern 1.5mu)\) and \(\Gamma^{\prime}\) a subgroup of the divisible hull of \(\Gamma\) (i.e. for each \(x \in \Gamma^{\prime}\) there exists a non-zero integer \(n\) such that \(\left.n x \in \Gamma\right)\). If \(X\) is not a translate of a semi-abelian subvariety of \(A\), then \(X(\mkern 1.5mu\overline{\mkern-1.5muK\mkern-1.5mu}\mkern 1.5mu) \cap \Gamma^{\prime}\) is not Zariski dense in \(X .\) 
