#### DOCUMENTA MATHEMATICA,
Extra Volume: Kazuya Kato's Fiftieth Birthday (2003), 565-584

** Nobushige Kurokawa, Hiroyuki Ochiai, and Masato Wakayama **
Absolute Derivations and Zeta Functions

Just as the function ring case we expect the existence of the coefficient
field for the integer ring. Using the notion of one element field in place
of such a coefficient field, we calculate absolute derivations of arithmetic
rings. Notable examples are the matrix rings over the integer ring, where
we obtain some absolute rigidity. Knitting up prime numbers via absolute
derivations we speculate the arithmetic landscape. Our result is only a
trial to a proper foundation of arithmetic.

2000 Mathematics Subject Classification: 11R27, 11R42, 14G10

Keywords and Phrases: absolute derivations, absolute mathematics, absolute schemes

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