## Kodai Mathematical Journal

### A note on the geometricity of open homomorphisms between the absolute Galois groups of p-adic local fields

Yuichiro Hoshi

#### Abstract

In the present paper, we prove that an open continuous homomorphism between the absolute Galois groups of p-adic local fields is geometric [i.e., roughly speaking, arises from an embedding of fields] if and only if the homomorphism is HT-preserving [i.e., roughly speaking, satisfies the condition that the pull-back by the homomorphism of every Hodge-Tate representation is Hodge-Tate].

#### Article information

Source
Kodai Math. J., Volume 36, Number 2 (2013), 284-298.

Dates
First available in Project Euclid: 27 June 2013

https://projecteuclid.org/euclid.kmj/1372337519

Digital Object Identifier
doi:10.2996/kmj/1372337519

Mathematical Reviews number (MathSciNet)
MR3081248

Zentralblatt MATH identifier
1328.11113

#### Citation

Hoshi, Yuichiro. A note on the geometricity of open homomorphisms between the absolute Galois groups of p -adic local fields. Kodai Math. J. 36 (2013), no. 2, 284--298. doi:10.2996/kmj/1372337519. https://projecteuclid.org/euclid.kmj/1372337519