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A Note on Ramification of the Galois Representation on the Fundamental Group of an Algebraic Curve, II

✍ Scribed by T. Oda

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
436 KB
Volume
53
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let (X) be a smooth proper connected algebraic curve defined over an algebraic number field (K). Let (\pi_{1}(\bar{X})), be the pro-l completion of the geometric fundamental group of (\bar{X}=X \otimes_{k} \bar{K}). Let (p) be a prime of (K), which is coprime to l. Assuming that (X) has bad reduction at (\mathfrak{p}) and the Jacobian variety of (X) has good reduction at (p), we describe the action of the inertia group (I_{p}) on the quotient groups of (\pi_{1}(\widetilde{X})), by the higher commutator subgroups. 1995 Academic Press. Inc.

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