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On the Fontaine–Mazur Conjecture for Number Fields and an Analogue for Function Fields

✍ Scribed by Joshua Brandon Holden

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 339 KB
Volume: 81
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2434

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✦ Synopsis

The Fontaine Mazur Conjecture for number fields predicts that infinite l-adic analytic groups cannot occur as the Galois groups of unramified l-extensions of number fields. We investigate the analogous question for function fields of one variable over finite fields, and then prove some special cases of both the number field and function field questions using ideas from class field theory, l-adic analytic groups, Lie algebras, arithmetic algebraic geometry, and Iwasawa theory.

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