Riemann-Roch for the ring Z

We show that by working over the absolute base S (the ca tegoric al version of the sphere spectrum) instead of S[+/- 1] improves our previous Riemann-Roch formula for Spec Z. The formula equates the (integer valued) Euler characteristic of an Arakelov divisor with the sum of the degree of the divisor (using logarithms with base 2) and the number 1, thus confirming the understanding of the ring Z as a ring of polynomials in one variable over the absolute base S, namely S[X X ],1 + 1 = X + X (2) .