Ben Rosenfield Iwasawa-Tate Theory

This will contain my notes on Iwasawa-Tate theory. This will be done first for number fields and simple algebras (a la Weil), giving some number theoretic results. The meat of these notes is a study of the Standard L-functions for GL(n). We extend this to arbitary simple algebras (a la Godement/Jacquet). This is a long term project. As of now, I have basically completed the first case. There are a number of minor points left implicit or unproven. This should clear up over time. The necessary representation theory for this part will be included in another note (maybe). At this point, I am only trying to get the words on paper, once I have enough written down, it will be reorganized. A is the adeles, J is the ideles. In the local theory, k will denote a local field, while in the global theory, k will be a global field and kv will denote a completion at the place v.