Abstract
Let k be an algebraically closed field of characteristic \(p > 3\). Let A be an abelian surface over k. Fix an integer \(n \ge 1\) such that \(p \not \mid n\) and let \(K^{[n]}\) be the n-th generalized Kummer variety associated to A. In this article, we show that the S-fundamental group scheme and the Nori’s fundamental group scheme of \(K^{[n]}\) are trivial.
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Acknowledgements
The author would like to thank Prof. Sukhendu Mehrotra for useful discussions. The research of the author is supported by the Prime Minister’s Research Fellowship (Application ID 1301167).
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Communicated by A J Parameswaran.
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Rasul, P. Fundamental group schemes of generalized Kummer variety. Proc Math Sci 133, 31 (2023). https://doi.org/10.1007/s12044-023-00750-6
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DOI: https://doi.org/10.1007/s12044-023-00750-6
Keywords
- Abelian surface
- S-fundamental group-scheme
- Kummer variety
- numerically flat locally free sheaf
- Tannakian category