Jean-Benoît Bost
Jean-Benoît Bost
Formal-analytic arithmetic surfaces and their applications
Abstract: Formal-analytic arithmetic surfaces are arithmetic analogues of germs of formal surfaces along a proper algebraic curve, in the same way as arithmetic surfaces are analogues of projective algebraic surfaces. It is possible to develop the Arakelov geometry of formal-analytic arithmetic surfaces, involving Hermitian vector bundles and suitably defined arithmetic intersection numbers. The arithmetic geometry of formal-analytic arithmetic surfaces admits applications to arithmetic algebraization theorems, closely related to the recent papers of Calegari, Dimitrov, and Tang, and also to finiteness results concerning the étale fundamental group of arithmetic surfaces, for instance of integral models of modular curves. This is joint work with F. Charles.