Relative fundamental groups and rational points
Rendiconti del Seminario Matematico della Università di Padova, Volume 134 (2015), pp. 1-46.
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Lazda, Christopher. Relative fundamental groups and rational points. Rendiconti del Seminario Matematico della Università di Padova, Volume 134 (2015), pp. 1-46. http://archive.numdam.org/item/RSMUP_2015__134__1_0/

[1] T. Abe, Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic 𝒟 -modules, preprint (2011), arXiv:math/1105.5796. | Numdam | MR | Zbl

[2] P. Berthelot, Cohomologie rigide et cohomologie rigide à supports propres, première partie, preprint (1996).

[3] P. Berthelot, 𝒟 -modules arithmétique I. Opérateurs différentiels de niveau fini, Ann. scient. Éc. Norm. Sup. 29 (1996), 185–272. | Numdam | MR | Zbl

[4] P. Berthelot, 𝒟 -modules arithmétique II. Descente par Frobenius, Mémoires de la SMF (2000), no. 81. | Numdam | Zbl

[5] P. Berthelot, Introduction à la théorie arithmétique des 𝒟 -modules, Cohomologies p -adiques et applications arithmétiques, II, no. 279, Astérisque, 2002, pp. 1–80. | Numdam | MR | Zbl

[6] D. Caro, 𝒟 -modules arithmétiques surcohérents. Applications aux fonctions L, Ann. Inst. Fourier, Grenoble 54 (2004), no. 6, 1943–1996. | Numdam | MR | Zbl

[7] D. Caro, Dévissages des F -complexes de 𝒟 -modules arithmétiques en F -isocristaux surconvergents, Inventiones math. 166 (2006), 397–456. | MR | Zbl

[8] D. Caro, F -isocristaux surconvergents et surcohérence differentielle, Inventiones math. 170 (2007), 507–539. | MR | Zbl

[9] D. Caro, 𝒟 -modules arithmétiques surholonomes, Ann. scient. Éc. Norm. Sup. 42 (2009), no. 1, 141–192. | Numdam | MR | Zbl

[10] D. Caro, Stabilité par produit tensoriel de la surholonomie, preprint (2012), arXiv: math/0605.125v5.

[11] D. Caro, Pleine fidélité sans structure de Frobenius et isocristaux partiellement surconvergents, Math. Ann. 349 (2011), no. 4, 747–805. | MR | Zbl

[12] D. Caro, Sur la préservation de la surconvergence par l’image directe d’un morphisms propre et lisse, preprint (2012), arXiv:math/0811.4740v3. | MR

[13] D. CaroN. Tsuzuki, Overholonomicity of overconvergent F -isocrystals over smooth varieties, Ann. of Math. 176 (2012), no. 2, 747–813. | MR | Zbl

[14] C. Chabauty, Sur les points rationnels des courbes algébriques de genre supérieur à l’unité, C. R. Acad. Sci. Paris 212 (1941), 882–885. | JFM | MR

[15] B. Chiarellotto, Weights in rigid cohomology applications to unipotent F-isocrystals, Ann. scient. Éc. Norm. Sup. 31 (1998), 683–715. | Numdam | MR | Zbl

[16] B. Chiarellotto and B. Le Stum, F-isocristaux unipotents, Compositio Math. 116 (1999), 81–110. | MR | Zbl

[17] B. Chiarellotto and B. Le Stum, Pentes en cohomologie rigide et F -isocristaux unipotents, Manuscripta Math. 100 (1999), 455–468. | MR | Zbl

[18] P. Deligne, Equations différentielles à points singuliers réguliers, Lecture Notes in Mathematics, vol. 168, Springer-Verlag, New York, 1970. | MR | Zbl

[19] P. Deligne, Le groupe fondamental de la droite projective moins trois points 1989, pp. 79–297. | MR | Zbl

[20] P. Deligne, Catégories tannakiennes, The Grothendieck Festschrift, Vol. II, Progress in Mathematics, vol. 87, Birkhäuser, 1990. | MR | Zbl

[21] A. DimcaF. MaarefC. SabbahM. Saito, Dwork cohomology and algebraic D-modules, Math. Ann. 318 (2000), no. 1, 107–125. | MR | Zbl

[22] H. EsnaultP. HaiX. Sun, On Nori’s fundamental group scheme, Geometry and Dynamics of Groups and Spaces, Progress in Mathematics, vol. 265, Birkhäuser, 2007, pp. 377–398. | MR | Zbl

[23] A. Borel et al., Algebraic D-modules, Perspectives in Mathematics, vol. 2, Academic Press Inc., 1987. | MR | Zbl

[24] M. Hadian-Jazi, Motivic fundamental groups and integral points, Ph.D. thesis, Universität Bonn, 2010. | MR | Zbl

[25] R. HainS. Zucker, Unipotent variations of mixed Hodge structure, Inventiones math. 88 (1987), 83–124. | MR | Zbl

[26] R. Hartshorne, On the de Rham cohomology of algebraic varieties, Publ. Math. I.H.E.S. 45 (1975), no. 1, 6–99. | Numdam | MR | Zbl

[27] N. Katz, Nilpotent Connections and the Monodromy Theorem: Applications of a result of Turrittin, Publ. Math. I.H.E.S. 39 (1970), 175–232. | Numdam | MR | Zbl

[28] M. Kim, The motivic fundamental group of 𝐏 1 {0,1,} and the theorem of Siegel, Inventiones math. 161 (2005), 629–656. | MR | Zbl

[29] M. Kim, The unipotent Albanese map and Selmer varieties for curves, Publ. RIMS, Kyoto Univ. 45 (2009), 89–133. | MR | Zbl

[30] S. Maclane, Categories for the working mathematician, Graduate Texts in Mathematics, vol. 5, Springer, 1971. | MR | Zbl

[31] J.S. Milne and P. Deligne, Tannakian categories, Hodge Cycles, Motives and Shimura Varieties, Lecture Notes in Mathematics, vol. 900, Springer, 1981, pp. 101–228. | Zbl

[32] V. Navarro Aznar, Sur la connection de Gauss–Manin en homotopie rationelle, Ann. scient. Éc. Norm. Sup. 26 (1993), 99–148. | Numdam | MR | Zbl

[33] J.-P. Serre, Local Fields, Translated from the French by Marvin Jay Greenberg, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, 1979. | MR | Zbl

[34] A. Tamagawa, Finiteness of isomorphism classes of curves in positive characterisitc with prescribed fundamental groups, J. Algebraic Geom. 13 (2004), 675–724. | MR | Zbl

[35] J. Wildeshaus, Realisations of polylogarithms, Lecture Notes in Mathematics, vol. 1650, Springer, 1997. | MR | Zbl