有限指数子格
Sublattices of finite index
摘要：
在有限参数$s$的Gowers逆猜想和Möbius猜想的假设下，Green-Tao证明了Dickson猜想对于复杂度至多为$s$的线性映射的格的猜想.本文将Green-Tao定理推广到Dickson猜想上，证明了：若$L$是复杂度为$s$的线性映射的值域，而$L_1$是$L$的有限指数子格，则$L_1$是复杂度为$s$的线性映射的值域.
英文摘要：
Assuming the Gowers Inverse conjecture and the Möbius 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 $s$.
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