$p$-adic space-time and string theory

Arguments are presented in favour of the hypothesis suggesting the $p$-adic structure of the space-time. A $p$-adic analogue of the Veneziano amplitude is suggested which makes it possible to start the construction of the theory of $p$-adic strings. The same problems are considered over Galois fields in which case the analogue of the Veneziano amplitude is the Jacobi sum expressed in terms of $l$-adic cohomologies of Fermat curves. An expression for the vertex operator of corresponding string theory is given.