All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Studying archeology or digging up the remnants of past human life and culture is religiously permissible and there is nothing wrong about it if this does not lead to a religious prohibition, like honouring the dead non-Muslims and the like. In principle all things are permissible [unless proven otherwise].
Furthermore, this science may lead to some benefits, like knowing the state of past nations and learning a lesson from it. Allaah Says (what means): {Say, [O Muhammad ], “Travel through the land and observe how was the end of those before. Most of them were associators [of others with Allaah].} [Quran 30:42]
However, it is not permissible to keep idols as this contradicts the Sharee’ah which ordered us to demolish and destroy them. Besides, it is not permissible to visit museums which contain prohibitions, like idols and the like, because it is not permissible for a Muslim to go to a place where there is a prohibition except for a valid purpose, like forbidding people from committing it for example.
For more benefit, please refer to Fatwa 84193.
As regards preserving mummies, they must be buried as Allaah Says (what means): {Then He causes him to die, then assigns to him a grave.}[Quran 80:21]
Moreover, the Prophet ordered us to hasten to bury the dead as he said: “Hasten to bury the dead.” [Al-Bukhari and Muslim] Therefore, keeping parts of the corpse unburied without a valid reason contradicts the Sharee’ah.
Allaah Knows best.