Today there are many impressions about the war crimes trials and most of them are false. So lets get some misconceptions cleared up.
No one term, not even the name Nuremberg, can summarize what they were. There was the International Military Tribunal conducted jointly by the four Allies. There were trials conducted separately by each of the Allies. There were national trials conducted by the liberated countries including Germany.
The purpose of these trials was not to prove the holocaust occurred. The camps and what happened in them were a small part of the most famous international trials and were rarely the primary focus of even the smallest trials. Gassing per se was not the focus of any trial.
Thus there are no official documents that directly discuss the matters that are subsumed by the "holocaust" today. What does exist is scattered over hundreds of official documents as well unofficial statements and writings of people afterwards. This perhaps excuses the holocaust writers for never presenting all never presenting all of the information but it can never excuse them for being so careful in what they exclude.
The trials conducted by the Allies went on for some three years in Europe. In national courts they continue to this day. Even Israel that did not even exist at the time conducts an occasional show trial against the innocent.
The joint trials held by the Allies under the name International Military Tribunal, commonly referred to as the Nuremberg trials, were largely for the commission of acts that were not crimes at the time they were committed as many well known and repected people have observed.
Nor were these trials conducted in any manner that an American citizen would consider fair. It is not simply that they were not read their rights and such recent additions to US law. There were clearly and regularly enough infractions of of Anglo-Saxon legal traditions that in the US would cause either mistrials or reversals on appeal.
You can go there or read a quick summary here.