Let be the quotient of a connected reductive algebraic C-group G by a finite subgroup Γ. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when Γ is nonabelian. Further, we construct an example of a homogeneous space X and an automorphism σ of C such that the topological fundamental groups of X and of the conjugate variety σX are not isomorphic.
Soit le quotient d'un C-groupe algébrique réductif connexe G par un sous-groupe fini Γ. On décrit le groupe fondamental topologique de l'espace homogène X, qui est non abélien quand Γ est non abélien. Puis on construit un exemple d'espace homogène X et d'automorphisme σ de C tels que les groupes fondamentaux topologiques de X et de la variété conjuguée σX ne sont pas isomorphes.
Accepted:
Published online:
Mikhail Borovoi 1; Yves Cornulier 2
@article{CRMATH_2015__353_11_1001_0, author = {Mikhail Borovoi and Yves Cornulier}, title = {Conjugate complex homogeneous spaces with non-isomorphic fundamental groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {1001--1005}, publisher = {Elsevier}, volume = {353}, number = {11}, year = {2015}, doi = {10.1016/j.crma.2015.09.010}, language = {en}, }
TY - JOUR AU - Mikhail Borovoi AU - Yves Cornulier TI - Conjugate complex homogeneous spaces with non-isomorphic fundamental groups JO - Comptes Rendus. Mathématique PY - 2015 SP - 1001 EP - 1005 VL - 353 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2015.09.010 LA - en ID - CRMATH_2015__353_11_1001_0 ER -
Mikhail Borovoi; Yves Cornulier. Conjugate complex homogeneous spaces with non-isomorphic fundamental groups. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1001-1005. doi : 10.1016/j.crma.2015.09.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.010/
[1] Faithful actions of the absolute Galois group on connected components of moduli spaces, Invent. Math., Volume 199 (2015), pp. 859-888
[2] Residually finite groups with the same finite images, Compos. Math., Volume 29 (1974), pp. 249-252
[3] The absolute Galois group acts faithfully on regular dessins and on Beauville surfaces, Proc. London Math. Soc. (2015) (in press) | DOI
[4] Nonhomeomorphic conjugates of connected Shimura varieties, Amer. J. Math., Volume 132 (2010), pp. 731-750
[5] An example of non-homeomorphic conjugate varieties, Math. Res. Lett., Volume 18 (2011), pp. 937-943
[6] Exemples de variétés projectives conjuguées non homéomorphes, C. R. Acad. Sci. Paris, Volume 258 (1964), pp. 4194-4196
Cited by Sources:
Comments - Policy