It has become recently a fashion to try to construct the ultimate theories of matter on the microscopic level (below the Planck scale) by considering some more exotic mathematical structures than those used usually by physicists. In particular, there are attempts to use the p- adic numbers to construct the higher-dimensional membrane theories with scattering amplitudes generalizing the Virasoro-Shapiro amplitudes of dual models. In the paper the previous description of membranes by p-adic algebraic extensions, due to J. L. Gervais, is generalized, using p-adic group theory, to obtain, by algebraic extensions, an arbitrarily high- dimensional cohomology (as determined by the factors of Artin-Mazur zeta function). As a second result the factorization of the inverse partition function for 26-dimensional bosonic string is interpreted as the existence of 11-dimensional membrane. Finally, it has become possible recently to prove the index theorems by constructing some supersymmetric sigma models; also recently discovered invariants for low-dimensional manifolds can be interpreted in terms of supersymmetric quantum models. According to this line of thought the author suggests the possibility of interpreting also the cohomological content of Weyl-Deligne theorem in terms of supersymmetric quantum mechanics (in its p-adic form). However, no model has been explicitly constructed, only some indications are given.