Integral models of P¹ and analytic distribution algebras for GL₂

In the first part of the paper we show that the ring of global sections of arithmetic differential operators on the formal projective line over Zp is isomorphic to the analytic distribution algebra of the 'wide open' congruence subgroup of level zero of GL(2,Zp). In the second part we study rings of logarithmic differential operators on semistable integral models of the projective line over Zp and we relate these to analytic distribution algebra of 'wide open' congruence subgroups of higher level.