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Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized surfaces
Author(s) -
Javanpeykar Ariyan
Publication year - 2015
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdu095
Subject(s) - mathematics , conjecture , genus , pure mathematics , reduction (mathematics) , good reduction , field (mathematics) , set (abstract data type) , algebra over a field , geometry , medicine , botany , surgery , computer science , biology , programming language
We prove the arithmetic Shafarevich conjecture for canonically polarized surfaces which fibre smoothly over a curve. Our proof uses (1) the theory of Néron models for hyperbolic curves, (2) classical results of Arakelov–Parshin and (3) Faltings's finiteness theorem for curves of fixed genus over a number field K with good reduction outside a fixed set of finite places of K .
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