Abstract
Let k be a field, A a finite k-algebra and X a smooth A-scheme. We describe the Galois set of connected components of the Weil restriction \(\mathfrak {R}_{A/ k}(X)\) in terms of the sets of connected components of the geometric fibers of X.
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References
Bertapelle, A., González-Avilés, C.D.: The Greenberg functor revisited. arXiv:1311.0051v3, (2014)
Bosch, S., Lütkebohmert, W., Michel, R.: Néron models, Volume 21 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, Berlin (1990)
Conrad, B., Gabber, O., Prasad, G.: Pseudo-reductive groups, Volume of 17 New Mathematical Monographs. Cambridge University Press, Cambridge (2010)
Demazure, M., Gabriel, P.: Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs. Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam (1970)
Grothendieck, A., Dieudonné, J.A.: Eléments de géométrie algébrique. I, volume 166 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin (1971)
Knutson, D.: Algebraic spaces. Lecture Notes in Mathematics, vol. 203. Springer-Verlag, Berlin, New York (1971)
Milne, J.S.: Étale cohomology, volume 33 of Princeton Mathematical Series. Princeton University Press, Princeton, N.J. (1980)
The Stacks Project Authors: Stacks Project. http://stacks.math.columbia.edu/
Acknowledgments
We thank the referee for suggesting the precise form that Theorem 1.2 should have and for encouraging us to prove this result. The first author was partially supported by PRAT 2013 “Arithmetic of varieties over number field”, CPDA 135371/13. The second author was partially supported by Fondecyt Grant 1120003.
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Bertapelle, A., González-Avilés, C.D. Galois sets of connected components and Weil restriction. Math. Z. 285, 607–612 (2017). https://doi.org/10.1007/s00209-016-1723-9
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DOI: https://doi.org/10.1007/s00209-016-1723-9