eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-12-04
11:1
11:14
10.4230/LIPIcs.FSTTCS.2019.11
article
Constructing Faithful Homomorphisms over Fields of Finite Characteristic
Chatterjee, Prerona
1
https://orcid.org/0000-0003-2643-8142
Saptharishi, Ramprasad
1
https://orcid.org/0000-0002-7485-3220
Tata Institute of Fundamental Research, Mumbai, India
We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken et al. [Malte Beecken et al., 2013] and exploited by them and Agrawal et al. [Manindra Agrawal et al., 2016] to design algebraic independence based identity tests using the Jacobian criterion over characteristic zero fields. An analogue of such constructions over finite characteristic fields were unknown due to the failure of the Jacobian criterion over finite characteristic fields.
Building on a recent criterion of Pandey, Saxena and Sinhababu [Anurag Pandey et al., 2018], we construct explicit faithful maps for some natural classes of polynomials in fields of positive characteristic, when a certain parameter called the inseparable degree of the underlying polynomials is bounded (this parameter is always 1 in fields of characteristic zero). This presents the first generalisation of some of the results of Beecken, Mittmann and Saxena [Malte Beecken et al., 2013] and Agrawal, Saha, Saptharishi, Saxena [Manindra Agrawal et al., 2016] in the positive characteristic setting.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol150-fsttcs2019/LIPIcs.FSTTCS.2019.11/LIPIcs.FSTTCS.2019.11.pdf
Faithful Homomorphisms
Identity Testing
Algebraic Independence
Finite characteristic fields