Fundamental groups and Diophantine geometry
Open Mathematics (2010)
- Volume: 8, Issue: 4, page 633-645
- ISSN: 2391-5455
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topMinhyong Kim. "Fundamental groups and Diophantine geometry." Open Mathematics 8.4 (2010): 633-645. <http://eudml.org/doc/269201>.
@article{MinhyongKim2010,
abstract = {This is a brief exposition on the uses of non-commutative fundamental groups in the study of Diophantine problems.},
author = {Minhyong Kim},
journal = {Open Mathematics},
keywords = {Fundamental group; Diophantine geometry; fundamental group},
language = {eng},
number = {4},
pages = {633-645},
title = {Fundamental groups and Diophantine geometry},
url = {http://eudml.org/doc/269201},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Minhyong Kim
TI - Fundamental groups and Diophantine geometry
JO - Open Mathematics
PY - 2010
VL - 8
IS - 4
SP - 633
EP - 645
AB - This is a brief exposition on the uses of non-commutative fundamental groups in the study of Diophantine problems.
LA - eng
KW - Fundamental group; Diophantine geometry; fundamental group
UR - http://eudml.org/doc/269201
ER -
References
top- [1] Coates J., Kim M., Selmer varieties for curves with CM Jacobians, preprint available at http://arxiv.org/abs/0810.3354 [WoS] Zbl1283.11092
- [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] Zbl1061.11034
- [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] Zbl1165.14020
- [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 Zbl1223.11080
- [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] Zbl1126.14035
- [8] Weil A., Généralisation des fonctions abéliennes, J. Math. Pures Appl., 1938, 17(9), 47–87 Zbl0018.06302
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