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Title: GALOIS-THEORETIC CHARACTERIZATION OF ISOMORPHISM CLASSES OF MONODROMICALLY FULL HYPERBOLIC CURVES OF GENUS ZERO
Authors: HOSHI, YUICHIRO  kyouindb  KAKEN_id
Author's alias: 星, 裕一郎
Issue Date: 2011
Publisher: Duke University Press
Journal title: Nagoya Mathematical Journal
Volume: 203
Start page: 47
End page: 100
Abstract: Let l be a prime number. In the present paper, we prove that the isomorphism class of an l-monodromically full hy-perbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-l outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to S. Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.
Rights: © 2011 Duke University Press
URI: http://hdl.handle.net/2433/148390
Related Link: http://projecteuclid.org/euclid.nmj/1313682312
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