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Calculus on formal-analytic arithmetic surfaces (live stream)

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Jean-Benoit Bost
Université Paris-Saclay
Mon, 22/07/2024 - 15:00 - 16:00
MPIM Lecture Hall

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.

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