Aise Johan de Jong -- Homepage

Picture of Aise Johan de Jong

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

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CURRENT AND FUTURE PROJECTS

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

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This semester I will teach a topics course. The topic will be etale cohomology of schemes.
I intend to work through the chapters [Arcata] and [Rapport] of SGA 4 1/2.
The class meets Tuesday and Thursday from 11-12:15 in Room 307 of the Mathematics Building.
There are now class notes, maintained by Thibaut Pugin et al.

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This semester the graduate student algebraic geometry seminar is on algebraic stacks.
We meet on Fridays from 10:30-12:30 in Room 312 of the Mathematics Building.
I will give the first two lectures to introduce the material, the first one on Friday, September 11.
After the first two lectures the graduate students will lecture on examples of algebraic stacks,
especially those which are relevant to moduli theory, and more generally arithmetic algebraic geometry.
Here is a (preliminary) list of topics for lectures by students: pdf | dvi | tex.
List of talks (see file above for more details):

There is a guide to the literature, written by Jarod Alper, see stacks_guide.pdf.

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The ALGEBRAIC STACKS PROJECT. Please visit its project page to learn more.

Here is a graph representing the logical implications in the computation of the cohomology groups
of the Serre twists of the structure sheaf on projective space: dependencies calculation cohomology projective space
The alphanumeric codes refer to tags in the project, explained in the tags system. Other images (some of them very large):

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PAST PROJECTS

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This summer I organized a conference on ``Spaces of curves and their interaction with diophantine problems''. Here is a link to the web page for the conference. Here is the schedule of talks. Here is the list of abstracts.

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This past semester the graduate student algebraic geometry seminar was organized by Maksym Fedorchuk and me. The topic was be Introduction to higher dimensional algebraic geometry. Here is some more information:

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This past semester I taught algebraic geometry, and in particular schemes (again, see below). See the webpage. As material I wrote some notes on schemes. See some of the files in the stacks project directory. This is a moving target (and probably contains errors) and I hope you will help me update it as the semester goes along.

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Two semesters ago the graduate student algebraic geometry seminar is organized by Frans Oort and me. The topic was ``Abelian Varieties over Finite Fields''. Main Literature Sources, with links:

Other links:

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Last semester I taught commutative algebra (again, see below). As material I wrote some algebra notes. See the file entitled algebra.pdf or algebra.dvi which you can find in the following directory. This is a moving target (and probably contains errors) and I hope you will help me update it as the semester goes along.

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The Fall semester of 2007 we discussed motives in the graduate student algebraic geometry seminar. Here are some related documents:

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Frobenius matrix computation project: see Frobenius. There is now an excecutable (compiled for generic x86 Linux machines) that you can try. Brief instructions: Download the executable, and save it as ``filename'' in a directory, change mode to executable, type ``./filename'' on the command line. Enjoy. Three versions:

Feel free to email me with questions/comments/etc.

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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 old webpage. Here is a link to the old webpage for the first semester of this course.

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I am nerdier than 94% of all people. Are you nerdier? Click here to find out!

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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.

OLD Calculus I web-pages:

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