Is there any evidence against these conspiracy theories?

American troops sort through German documents needed as evidence in war crime cases.

Yes, the most important evidence is not anything that is written out, it is the verbal confessions of many Nazis and SS members that validate the facts historians have formulated over the years. Einstzgruppe commander Otto Ohlendorf admitted that he and his troupe killed about 90,000 people within 1941 and 1942. This kind of evidence is what deniers, such as Paul Rassiner, believed the Allies were creating by torturing people into being involved. Deniers did not believe people would so easily confess to committing a war crime since they knew the penalty was death. Rudolf Hoss, the Birkenau concentration camp Nazi Commandant, was given the death penalty and decided to write e a paper full of in-depth descriptions on the killings that took place under his command. Additionally, Adolf Eichmann, Hitler’s partner in planning the extermination of the Jews, admitted that the gas chambers were, in fact, meant to mass-murder large groups of people in the concentration camps.The documents that all deniers either disregard or claim to be forged include a multitude of facts that make it blatantly obvious the Holocaust happened. On April 11, 1942, SS-Major General Dr Harald Turner wrote to the head of Himmler’s personal staff, Karl Wolff, about a “‘delousing van’” and how in four weeks it has done really well at “clearing out the camp.” Other letters were found about the buses and how “loads of 97,000 had been processed.” Along with these documents, Auschwitz death camp’s architectural documentations draw more attention from deniers than almost any other source of evidence. For example, a written order was discovered from February 1943 about twelve gas-tight doors and windows, with handles only on the outside, being installed in the camp. Deniers are convinced that the Nazis are talking about delousing chambers, morgues, or air-raid shelters, not gas chambers.