UnramDeg3 for GAP 4 ver.2019.09.26

Authors: Akinari Hoshi, Aiichi Yamasaki.
Needs: GAP, version >=4.8.7; GAP package HAP, version >=1.11.15;
Current version: UnramDeg3-2019.09.26.zip (Hnminus1QoverZtoHnZfromResolution in H3nr.gap was modified)
Old version: UnramDeg3ver.2017.09.09.zip
Contact: Akinari Hoshi, Aiichi Yamasaki.
Repository: KURENAI (Kyoto University Research Information Repository) https://doi.org/10.57723/289561
URL:
http://mathweb.sc.niigata-u.ac.jp/~hoshi/Algorithm/UnramDeg3/index.html
https://www.math.kyoto-u.ac.jp/~yamasaki/Algorithm/UnramDeg3/index.html

Description

This code provides algorithms for computing unraified and stable cohomologies of degree 3 for fields of invariants.

Installation

Download UnramDeg3-2019.09.26.zip and unpack it to some folder , e.g. C:\Users\username.
Then type "Read("H3nr.gap");" on GAP.

Documentation

H3nr [.html, .pdf]
README [.html, .pdf]

Content

UnramDeg3-2019.09.26.zip-+-H3nr.gap
                         +-H3nr.pdf
                         +-README.txt
                         +-README.pdf
                         +-UnramDeg3-2019.09.26.pdf

References

[HKY20] Akinari Hoshi, Ming-chang Kang and Aiichi Yamasaki, Degree three unramified cohomology groups and Noether's problem for groups of order 243, J. Algebra 544 (2020) 262-301. ScienceDirect Extended version: arXiv:1710.01958.

[Pe08] Emmanuel Peyre, Unramified cohomology of degree 3 and Noether's problem, Invent. Math. 171 (2008) 191-225.