John Baez提供了关于P进数很好的入门教学,可以通过本链接查阅。
A "Rosetta Stone"
Geometry | Function Fields | Number Theory |
---|---|---|
"Riemann sphere" | \mathbb{C}(X) | \mathbb{Q} |
complex plane | \mathbb{C}[X] | \mathbb{Z} |
point \alpha \in \mathbb{C} | irreducible X - \alpha | prime p |
Riemann surface | finite extension K/\mathbb{C}(X) | finite extension K/\mathbb{Q} |
"local" behavior | Laurent series around \alpha | !? |