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A note on ramification of the Galois representation on the fundamental group of an algebraic curve

✍ Scribed by Takayuki Oda

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
160 KB
Volume
34
Category
Article
ISSN
0022-314X

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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 \(X\) ha

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## Abstract In Β§ l of this article, we study group‐theoretical properties of some automorphism group Ξ¨^\*^ of the meta‐abelian quotient Β§ of a free pro‐__l__ group Β§ of rank two, and show that the conjugacy class of some element of order two of Ξ¨^\*^ is not determined by the action induced on the a