$F$-sets and finite automata
作者: Jason BellRahim Moosa
刊名: Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.101-130
来源数据库: The Center for Diffusion of Academic Mathematical Journals
DOI: 10.5802/jtnb.1070
关键词: Automatics sets$F$-setsSemiabelian varietiesPositive characteristic Mordell–LangSkolem–Mahler–Lech
原始语种摘要: It is observed that Derksen’s Skolem–Mahler–Lech theorem is a special case of the isotrivial positive characteristic Mordell-Lang theorem due to the second author and Scanlon. This motivates an extension of the classical notion of a $k$-automatic subset of the natural numbers to that of an $F$-automatic subset of a finitely generated abelian group $\Gamma $ equipped with an endomorphism $F$. Applied to the Mordell–Lang context, where $F$ is the Frobenius action on a commutative algebraic group $G$ over a finite field, and $\Gamma $ is a finitely generated $F$-invariant subgroup of $G$, it is shown that the “$F$-subsets” of $\Gamma $ introduced by the second author and Scanlon are $F$-automatic. It follows that when $G$ is semiabelian and $X\subseteq G$ is a closed subvariety then $X\cap...
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关键词翻译
关键词翻译
  • endomorphism 内变质酌
  • commutative 可换的
  • subvariety 亚变种
  • theorem 定理
  • automatic 自动的
  • group 
  • extended 扩展
  • introduced 引种的
  • subset 子集
  • automata 自动机