Chunlei Liu
Published 2006-12-15, updated 2007-01-05Version 4
Assuming the Gowers Inverse conjecture and the M\"{o}bius conjecture for the finite parameter $s$, Green-Tao verified Dickson's conjecture for lattices which are ranges of linear maps of complexity at most $s$. In this paper, we reformulate Green-Tao's theorem on Dickson's conjecture, and prove that, if $L$ is the range of a linear map of complexity $s$, and $L_1$ is a sublattice of $L$ of finite index, then $L_1$ is the range of a linear map of complexity $s$.
Comments: Revised on Jan. 5, 2007
$Λ$-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves
Counting Subrings of ${\mathbb Z}^n$ of finite index
Most subrings of $\mathbb{Z}^n$ have large corank
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