What distinguishes an arithmetic problem from a geometric one is the nature of the ground ring or ground field and any prime structure it may have. In addition to the existence of primes (prime numbers, prime ideals, etc.) one must also, or even principally, take into account archimedean absolute values. It turns out that all the foundational material we need can be stated in terms of absolute values, and we have included in this chapter everything we need in the sequel.
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