Abstract. In the present paper we consider countable state p-adic Potts model on the Cayley tree. A construction of p-adic Gibbs measures which depends on weights λ is given, and an investigation of such measures is reduced to examination of an infinite-dimensional recursion equation. Studying of the derived equation under some condition on weights, we prove absence of the phase transition. Not...

v det([1− ρ(Frobv)q v ]|W Iv )−1, W Iv = subspace of W fixed by inertia at v. Grothendieck gave a related description of ζ∗ X using continuous p-adic representations GF → GL(H ét,c(XF ,Qp)) =: GL(W ). These are unramified almost everywhere, including at all good places away from p. Here the ith cohomology group W i above vanishes for i > 2 dimX. Grothendieck proved that if we remove the contrib...

This paper is the first one in the series devoted to the calculation of particle mass spectrum in Topological GeometroDynamics. In this paper p-adic conformal field theory limit of TGD is formulated. TGD Universe is critical at quantum level and the idea is to realize criticality via conformal invariance. Ordinary real numbers do not allow this but if one assumes that in long length scales p-ad...