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math.AG2009★ 36 cited
Characteristic one, entropy and the absolute point
Alain Connes, Caterina Consani
We show that the mathematical meaning of working in characteristic one is directly connected to the fields of idempotent analysis and tropical algebraic geometry and we relate this…
math.AG2009★ 79 cited
Schemes over $\F_1$ and zeta functions
Alain Connes, Caterina Consani
We determine the {\em real} counting function () for the hypothetical "curve" $C=\overline {\Sp \Z}$ over $\F_1$, whose corresponding zeta function is the c…