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Register a new userRational map $ax+1/x$ on the projective line over $mathbb{Q}_{p}$
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Shilei Fan
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The dynamical structure of the rational map $ax+1/x$ on the projective line $P$ over the field $mathbb{Q}_p$ of $p$-adic numbers is described for $pgeq 3$.
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The dynamical structure of the rational map $ax+1/x$ on the projective line over the field Q2 of $2$-adic numbers, is fully described.
In this essay we study various notions of projective space (and other schemes) over $mathbb{F}_{1^ell}$, with $mathbb{F}_1$ denoting the field with one element. Our leading motivation is the Hiden Points Principle, which shows a huge deviation between the set of rational points as closed points defined over $mathbb{F}_{1^ell}$, and the set of rational points defined as morphisms $texttt{Spec}(mathbb{F}_{1^ell}) mapsto mathcal{X}$. We also introduce, in the same vein as Kurokawa [13], schemes of $mathbb{F}_{1^ell}$-type, and consider their zeta functions.
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