http://mathoverflow.net/questions/38066/which-languages-could-appear-on-weils-rosetta-stone
http://mathoverflow.net/questions/25975/is-there-an-arithmetic-cobordism-category
The two books of Neukirch contain some useful basics
Can we use for some arithmetic applications, the general philosophy that from the right perspective, everything is affine, and from the right perspective, everything is smooth?
Can we use functoriality wrt correspondences for understanding/computing CTs of arithmetic schemes?
nLab page on Arithmetic mysteries