Calculus on formal-analytic arithmetic surfaces (live stream)

Formal-analytic arithmetic surfaces are arithmetic analogues of germs of formal surfaces along a proper curve over some base field, in the same way as arithmetic surfaces are analogues of projective algebraic surfaces over some base field. It is possible to develop a  calculus  on formal-analytic arithmetic surfaces, involving Hermitian vector bundles and suitably defined arithmetic intersection numbers à la Arakelov. This calculus admits applications to finiteness results concerning the étale fundamental group of arithmetic surfaces, notably of integral models of modular curves. This is joint work with F. Charles.