## Kodai Mathematical Journal

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

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

#### 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

**Permanent link to this document**

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