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Sergey Nikolenko

Sergey Nikolenko

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Algebraic geometry and ChowMaple

Bio excerpt

In 2004, I was visiting Bielefeld University for two months and met Kirill Zainoulline and Nikita Semenov, who were working on motive theory there. They introduced me to the problems, and we were able to program a Maple package which could multiply elements of the Chow ring. The results were quite interesting: we were able to decompose the motives of projective homogeneous varieties F4/P1 and F4/P4, providing an explicit decomposition. We also proved their motivic isomorphism (while the varieties themselves are not isomorphic).

In 2005, we redesigned some of the algorithms, and the program was able to handle E6/P1, E6/P6, and E8/P8.

ChowMaple package

The package requires John Stembridge's coxeter and weyl packages which are available here. Here you can download the ChowMaple package itself and a brief manual on how to use it. It may still change, as I do not think it is very user-friendly right now. Please note that the package saves its results on your HDD, so do not be alarmed if a large file entitled polys.txt or multiply.txt suddenly appears. It has been so designed to avoid unnecessary (and very lengthy) computations.

Publications

  1. S.I. Nikolenko, N. Semenov, K. Zainoulline. Motivic decomposition of anisotropic varieties of type F4 into generalized Rost motives. Journal of K-Theory, vol. 3, 2009, pp. 85-102 (.pdf, 181kb)
  2. S.I. Nikolenko, N. Semenov, K. Zainoulline. Motivic decomposition of anisotropic varieties of type F4 and generalized Rost motives. ArXiv preprint. (.pdf, 215kb)
  3. S.I. Nikolenko, N. Semenov. Chow ring structure made simple. ArXiv preprint. (.pdf, 783kb)