Mordell-Lang in positive characteristic
Rendiconti del Seminario Matematico della Università di Padova, Volume 134 (2015), p. 93-132
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@article{RSMUP_2015__134__93_0,
     author = {Ziegler, Paul},
     title = {Mordell-Lang in positive characteristic},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {134},
     year = {2015},
     pages = {93-132},
     mrnumber = {3428416},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2015__134__93_0}
}
Ziegler, Paul. Mordell-Lang in positive characteristic. Rendiconti del Seminario Matematico della Università di Padova, Volume 134 (2015) pp. 93-132. http://www.numdam.org/item/RSMUP_2015__134__93_0/

[1] Schémas en groupes. I: Propriétés générales des schémas en groupes. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 151. Springer-Verlag, Berlin, 1970. | Zbl 0207.51401

[2] D. Abramovich and J. F. Voloch. Toward a proof of the Mordell-Lang conjecture in characteristic p. Internat. Math. Res. Notices, (5):103–115, 1992. | MR 1162230 | Zbl 0787.14026

[3] M. F. Atiyah and I. G. Macdonald. Introduction to commutative algebra. AddisonWesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. | MR 242802 | Zbl 0175.03601

[4] V. G. Berkovich. Vanishing cycles for formal schemes. II. Invent. Math., 125(2):367–390, 1996. | MR 1395723 | Zbl 0852.14002

[5] N. Bourbaki. Topologie générale. Chapitres 1 à 4. Hermann, Paris, 1971. | MR 358652

[6] N. Bourbaki. Commutative algebra. Chapters 1–7. Springer-Verlag, Berlin, 1989. | MR 979760 | Zbl 0666.13001

[7] B. Conrad. Irreducible components of rigid spaces. Ann. Inst. Fourier (Grenoble), 49(2):473–541, 1999. | Numdam | MR 1697371 | Zbl 0928.32011

[8] B. Conrad. Chow’s K/k-image and K/k-trace, and the Lang-Néron theorem. Enseign. Math. (2), 52(1-2):37–108, 2006. | MR 2255529 | Zbl 1133.14028

[9] A. J. De Jong. Crystalline Dieudonné module theory via formal and rigid geometry. Inst. Hautes Études Sci. Publ. Math., (82):5–96 (1996), 1995. | Numdam | MR 1383213 | Zbl 0864.14009

[10] M. Demazure. Lectures on p-divisible groups. Lecture Notes in Mathematics, Vol. 302. Springer-Verlag, Berlin, 1972. | MR 344261 | Zbl 0247.14010

[11] M. Demazure and A. Grothendieck (ed.). Schémas en groupes II (SGA 3), Lecture Notes in Mathematics, Vol. 152. Springer-Verlag, 1970. | Zbl 0209.24201

[12] D. Eisenbud. Commutative algebra. Springer-Verlag, New York, 1995. | MR 1322960 | Zbl 0819.13001

[13] G. Faltings and C.-L. Chai. Degeneration of abelian varieties. Springer-Verlag, Berlin, 1990. | MR 1083353 | Zbl 0744.14031

[14] D. Ghioca and R. Moosa. Division points on subvarieties of isotrivial semiabelian varieties. Int. Math. Res. Not., pages Art. ID 65437, 23, 2006. | MR 2264715 | Zbl 1119.14017

[15] A. Grothendieck. Éléments de géométrie algébrique. I. Le langage des schémas. Inst. Hautes Études Sci. Publ. Math., (4):228, 1960. | Zbl 0135.39701

[16] A. Grothendieck. Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II. Inst. Hautes Études Sci. Publ. Math., (24):231, 1965. | Numdam | MR 199181 | Zbl 0135.39701

[17] M. Hazewinkel. Formal groups and applications, volume 78 of Pure and Applied Mathematics. Academic Press Inc., New York, 1978. | MR 506881 | Zbl 0454.14020

[18] E. Hrushovski. The Mordell-Lang conjecture for function fields. J. Amer. Math. Soc., 9(3):667–690, 1996. | MR 1333294 | Zbl 0864.03026

[19] C. Kappen. Uniformly rigid spaces. Algebra Number Theory, 6(2):341–388, 2012. | MR 2950157 | Zbl 1254.14025

[20] W. Messing. The crystals associated to Barsotti-Tate groups: with applications to abelian schemes. Lecture Notes in Mathematics, Vol. 264. Springer-Verlag, Berlin, 1972. | MR 347836 | Zbl 0243.14013

[21] F. Oort. Subvarieties of moduli spaces. Invent. Math., 24:95–119, 1974. | MR 424813 | Zbl 0259.14011

[22] F. Oort and T. Zink. Families of p-divisible groups with constant Newton polygon. Doc. Math., 7:183–201 (electronic), 2002. | MR 1938119 | Zbl 1022.14013

[23] R. Pink and D. Rössler. On c-invariant subvarieties of semiabelian varieties and the Manin-Mumford conjecture. J. Algebraic Geom., 13(4):771–798, 2004. | MR 2073195 | Zbl 1072.14054

[24] D. Rössler. On the Manin-Mumford and Mordell-Lang conjectures in positive characteristic. Algebra Number Theory, 7(8):2039–2057, 2013. | MR 3134042 | Zbl 1295.14024

[25] T. Scanlon. A positive characteristic Manin-Mumford theorem. Compos. Math., 141(6):1351–1364, 2005. | MR 2185637 | Zbl 1089.03030

[26] The Stacks Project Authors. stacks project. http://stacks.math.columbia.edu, 2013.

[27] C. A. Weibel. An introduction to homological algebra. Cambridge University Press, Cambridge, 1994. | MR 1269324 | Zbl 0834.18001