@article{42010703fbdb4bd6862c1025b9cd942f,
title = "Imaginaries in separably closed valued fields",
abstract = "We show that separably closed valued fields of finite imperfection degree (either with λ-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets to study stably dominated types in those structures. We show that separably closed valued fields of finite imperfection degree are metastable and that the space of stably dominated types is strict pro-definable.",
author = "Martin Hils and Moshe Kamensky and Silvain Rideau",
note = "Funding Information: Received 16 March 2017; revised 27 September 2017; published online 1 February 2018. 2010 Mathematics Subject Classification 03C60 (primary), 12J20, 03C45, 03C98, 03C10 (secondary). The first author was partially supported by ANR through ValCoMo (ANR-13-BS01-0006) and by DFG through SFB 878. The second author was partially supported by ISF through grant no. 1382/15, and by ERC through FP7/2007-2013, (ERC Grant agreement no. 291111). The latter grant also funded a visit of the first author to Jerusalem in spring 2015 during which part of this research was carried out. The third author was partially supported by ANR through ValCoMo (ANR-13-BS01-0006). Funding Information: This collaboration began during the Spring 2014 MSRI program Model Theory, Arithmetic Geometry and Number Theory. The authors would like to thank MSRI for its hospitality and stimulating research environment. We are grateful to the referee for a thorough reading of our paper and many useful suggestions. Publisher Copyright: {\textcopyright} 2018 London Mathematical Society",
year = "2018",
month = jun,
day = "1",
doi = "10.1112/plms.12116",
language = "English",
volume = "116",
pages = "1457--1488",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "John Wiley and Sons Ltd",
number = "6",
}