A note on the geometricity of open homomorphisms between the absolute Galois groups of <i>p</i>-adic local fields
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In the present paper, we prove that an open continuous homomorphism between the absolute Galois groups of <i>p</i>-adic local fields is <i>geometric</i> [i.e., roughly speaking, arises from an embedding of fields] if and only if the homomorphism is <i>HT-preserving</i> [i.e., roughly speaking, satisfies the condition that the pull-back by the homomorphism of every Hodge-Tate representation is Hodge-Tate].
- Kodai Mathematical Journal
Kodai Mathematical Journal 36(2), 284-298, 2013
Department of Mathematics, Tokyo Institute of Technology