The six-functor formalism for rigid analytic motives

We offer a systematic study of rigid analytic motives over general spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that are able to justify by reducing the case algebraic motives. In fact, more generally, powerful technique for questions about motives, which likely be useful in other contexts as well. pay special attention establishing our results without noetherianity assumptions on spaces. This indeed possible using Raynaud's approach geometry.