Aise Johan de Jong -- Homepage

Professor A.J. de Jong, Columbia university, Department of Mathematics.

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Calculus I students please go here:

• The webpage.
• The Columbia University Directory of Classes: Calculus I
• Courseworks: Calculus I
• Webworks: Calculus I

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The algebraic geometry seminar at Columbia is organized by Micheal Thaddeus (and Friedman/me).

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Special workshop at Stony Brook organized by Jason Starr (and Tschinkel/Hassett/me). See web-page.

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The graduate student algebraic geometry seminar is held Fridays 10:30-12:30 in room 312 of the mathematics building. This semester I am giving a series of lectures with the aim of formulating a bunch of problems that graduate students can view as starting points for research. The first meeting is on Friday January 22. Please e-mail me for more information, and to get on the mailing list.

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Last semester we discussed motives in the seminar. Here are some related documents:

• and a list of literature is here.
• A short discussion of intersection theory (as used in the seminar) is here.
• A short discussion of Weil cohomology theories (as used in the seminar) is here.
• A short discussion of algebraic de Rham cohomology as a Weil cohomology theory is here.

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Very preliminary work is being done on open source web-based math development on this page. Take a look! Also take a look at the associated mailing list and more interestingly its archives.

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Frobenius matrix computation project: see Frobenius

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A while ago I taught algebraic geometry which was a second semester of an introductory graduate course in algebraic geometry. Having gone through a substantial amount of commutative algebra in the first semester, we used this material to build the foundations of modern algebraic geometry (schemes). Here is the webpage. Here is a link to the webpage for the first semester of this course.

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Here is a list of papers/projects with links to the .dvi-files of some of the papers. Note that the .dvi files are not always identical with the published version (but they are very close), as in some cases editing was done after proof reading the proofs from the journal in question.

• A.J. de Jong, Th. de Jong, The virtual number of D-infinity points II, Topology, 29 (1990), pp. 185-188.
• A.J. de Jong, N.I. Sheperd-Barron, A. Van de Ven, On the Burkhardt quartic, Mathematische Annalen, 286 (1990), pp. 309-328.
• A.J. de Jong, R. Noot, Jacobians with complex multiplications, In: Arithmetic Algebraic Geometry, Eds. G. van der Geer, F. Oort, J.H.M. Steenbrink, Progress in Mathematics, 89 (1991), Birkh\"auser, pp. 177-192.
• A.J. de Jong, J.H.M. Steenbrink, Picard numbers of surfaces in 3-dimensional weighted projective spaces, Mathematisches Zeitschrift, 206 (1991), pp. 341-344.
• A.J. de Jong, The moduli spaces of polarized abelian varieties, Mathematische Annalen, 295 (1993), pp. 485-503. papers/AGEE.dvi
• A.J. de Jong, The moduli spaces of principally polarized abelian varieties with $\Gamma_0(p)$-level structure, Journal of Algebraic Geometry, 2 (1993), pp. 667-688. papers/SGEE.dvi
• A.J. de Jong, Finite locally free group schemes in characteristic $p$ and Dieudonn\'e modules, Inventiones mathematicae, 114 (1993), pp. 89-137. papers/DIEUDONNEE.dvi
• A.J. de Jong, Ample line bundles and intersection theory, In: Diophantine approximation and Abelian varieties, Eds. B. Edixhoven, J.-H. Evertse, Lecture Notes in Mathematics, 1566 (1993), Springer-Verlag, pp. 69-76. papers/SOESTERBERG.dvi
• A.J. de Jong, J.H.M. Steenbrink, Proof of a conjecture of W. Veys, Indagationes Mathematicae, N.S., 6 (1995), pp. 99-104.
• A.J. de Jong, M. van der Put, \'Etale cohomology of rigid spaces, Documenta Mathematica (electronic journal), 1 (1996), pp. 1--56. papers/RIGETALE.dvi
• A.J. de Jong, Crystalline Dieudonn\'e module theory via formal and rigid geometry, Publications Mathematiques I.H.E.S., 82 (1995), pp. 5-96. papers/FORMALRIGID.dvi
  Here is an erratum: /papers/erratum.dvi
• M. Pikaart, A.J. de Jong, Moduli of curves with non-abelian level structures, In: The moduli spaces of curves, Eds. R. Dijkgraaf, C. Faber, G. van der Geer, Progress in Mathematics, 129 (1995), Birkh\"auser, pp. 483-509. papers/MARTIN.dvi
• A.J. de Jong, W. Messing, Crystalline Dieudonn\'e theory over excellent schemes, Bull. Soc. Math. France 127, no. 2, 333--348 (1999). papers/MESSING.dvi
• A.J. de Jong, \'Etale fundamental groups of non-Archimedean analytic spaces, In: Special issue of Compositio in honour of Frans Oort, Compositio Mathematica, 97 (1995), 89-118. papers/ETALEFUN.dvi
• A.J. de Jong, F. Oort, On extending families of curves, Journal of Algebraic Geometry, 6 (1997), pp. 545--562. papers/EXTFAMCURVES.dvi
• A.J. de Jong, A result on formal linearity, Journal of Algebra 225, no. 2, pp. 936--942 (2000). papers/FORMALLINEAR.dvi
• A.J. de Jong, Smoothness, semi-stability and alterations, Publications Mathematiques I.H.E.S., 83(1996), pp. 51-93. papers/ALTERATIONS.dvi
• B. van Geemen, A.J. de Jong, On Hitchin's connection, Journal of the American Mathematical Society, 11 (1998), pp. 189--228. papers/BERT.dvi
• A.J. de Jong, Appendix to a paper by P. Berthelot on finiteness of rigid cohomology, Published as appendix to: P. Berthelot, Finitude et puret\'e cohomologique en cohomologie rigide, Inventiones Mathematicae, 128 (1997), 329--377.
• A.J. de Jong, Homomorphisms of Barsotti-Tate groups and crystals in positive characteristic, Inventiones Mathematicae, 134 (1998). papers/TATE.dvi
  Here is an erratum: papers/ErratumTate.dvi
• F. Oort, A.J. de Jong, Hyperelliptic curves in Abelian Varieties, Published in: "Manin's Festschrift", Journal of mathematical sciences, 82 (1997), pp. 141--166. papers/HYPERELL.dvi
• A.J. de Jong, Families of curves and alterations, Annales de l'institute Fourier, 47 (1997), pp. 599--621. papers/ALTCURVES.dvi
• D. Abramovich, A.J. de Jong, Smoothness, semi-stability and toroidal geometry, Journal of Algebraic Geometry, 6 (1997), pp. 789-801. papers/RESOLVE.dvi
• A.J. de Jong, A conjecture on arithmetic fundamental groups, Israel Journal of Mathematics. {\bf 121}, 61--84 (2001). papers/ARITHFUN.dvi
• A.J. de Jong, Barsotti-Tate groups and crystals, Proceedings ICM 1998 (Berlin), volume II, pp. 259--265. papers/ICM.dvi
• A.J. de Jong, An application of alterations to Dieudonn\'e modules, Resolution of singularities (Obergurgl, 1997), 375--380, Progr. Math., 181, Birkhauser, Basel, 2000. papers/OBERG.dvi
• A.J. de Jong, F. Oort, Purity of the stratification by Newton Polygons, J. Amer. Math. Soc. 13, no. 1, 209--241 (2000). papers/NEWTON.dvi
• A.J. de Jong, N.M. Katz, Monodromy and the Tate conjecture: Picard numbers and Mordell-Weil ranks in families, Israel J. Math. {\bf 120}, part A, 47--79 (2000).
• A.J. de Jong, J. Starr, Every rationally connected variety over the function field of a curve has a rational point, American Journal of Mathematics, {\bf 125}, 567--580 (2003). familyofcurves3.dvi
  Here is the ad hoc argument showing how to obtain reduced fibres after base change which was in theoriginal version of the preprint: alternative.dvi
• A.J. de Jong, The period-index problem for the Brauer group of an algebraic surface, Duke Mathematical Journal, 123, 71--94 (2004). perind.dvi
• A.J. de Jong, Counting elliptic surfaces over finite fields, Moscow Mathematical Journal, 2, 281--381 (2002). surfaces2.dvi
• B. Conrad and A.J. de Jong, Approximation of versal deformations, Journal of Algebra, 255, no. 2, 489--515 (2002). approximation.dvi
• A.J. de Jong, J. Starr, Cubic fourfolds and spaces of rational curves, Illinois Journal of Mathematics, 48 (2004), pp. 415--430.
• A.J. de Jong, A result of Gabber,Preprint with missing references about Br=Br' on quasiprojective schemes. 2-gabber.dvi or 2-gabber.pdf
• J. Starr, A.J. de Jong, A remark on isotrivial families, Preprint with missing references, precursor of the next entry. JasonsTrick_final.pdf
• J. Starr, A.J. de Jong, Almost proper GIT-stacks and discriminant avoidance, Preprint with missing references and misleading title. This paper also handles the period-index problem for Brauer groups of surfaces over any algebraically closed field. 5-torsor.pdf
• A.J. de Jong, Shioda cycles in families of surfaces, Preprint on work in progress: Shioda.dvi
• A.J. de Jong and N.M. Katz Counting the number of curves over a finite field. This unpublished note was written probably around the time I was in Princeton (1998-2000) since it resulted from discussions with Nick katz. It gives the trivial upper bound for the number of isomoprhism classes of genus g curves over F_q. Here is a link: curves.dvi.