In order to support a "working hypothesis" on mind_matter relationships I am looking for a formalization of the concept of noosphere by relying on relativistic and quantum concepts. I start from an idea which consists of keeping the model of General Relativity defined on a four-dimensional Riemanian variety while considering that its dimensions Xα are complex, in other words that it is a Hermitian space. The rest in the linked page, sorry in French. ChatGPT should be able to translate it for English speakers.