Fundamental groups and Diophantine geometry

• Autorzy: Minhyong Kim
• Języki publikacji: EN

Abstrakty

EN

This is a brief exposition on the uses of non-commutative fundamental groups in the study of Diophantine problems.

Słowa kluczowe

EN

Fundamental group; Diophantine geometry

Kategorie tematyczne

• 14G25: Global ground fields

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 4
• Strony: 633-645

Daty

wydano

2010-08-01

online

2010-07-24

Twórcy

autor

Minhyong Kim

• University College London, London, UK,

Bibliografia

• [1] Coates J., Kim M., Selmer varieties for curves with CM Jacobians, preprint available at http://arxiv.org/abs/0810.3354 [WoS]
• [2] Deligne P., Le groupe fondamental de la droite projective moins trois points, In: Galois groups over ℚ, Berkeley, 1987, Math. Sci. Res. Inst. Publ., 16, Springer, New York, 1989, 79–297 [Crossref]
• [3] Furusho H., p-adic multiple zeta values. I: p-adic multiple polylogarithms and the p-adic KZ equation, Invent. Math., 2004, 155(2), 253–286 http://dx.doi.org/10.1007/s00222-003-0320-9[Crossref]
• [4] Kim M., The motivic fundamental group of ℙ1 \ {0; 1;∞} and the theorem of Siegel, Invent. Math., 2005, 161(3), 629–656 http://dx.doi.org/10.1007/s00222-004-0433-9
• [5] Kim M., The unipotent Albanese map and Selmer varieties for curves, Publ. Res. Inst. Math. Sci., 2009, 45(1), 89–133 http://dx.doi.org/10.2977/prims/1234361156[WoS][Crossref]
• [6] Kim M., p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication, Ann. of Math., (in press), preprint available at http://arxiv.org/abs/0710.5290
• [7] Kim M., Tamagawa A., The ℓ-component of the unipotent Albanese map, Math. Ann., 2008, 340(1), 223–235 http://dx.doi.org/10.1007/s00208-007-0151-x[Crossref][WoS]
• [8] Weil A., Généralisation des fonctions abéliennes, J. Math. Pures Appl., 1938, 17(9), 47–87

Identyfikatory

DOI

10.2478/s11533-010-0047-y