The Southwest Center for Arithmetic Geometry
Arizona Winter School 1999
Course Descriptions and Notes


“The localglobal principle” project
description: dvi, ps,
pdf

References for
talks: dvi, ps, pdf

Slides for Barbu's talk on the Brauer
group: dvi, ps, pdf


“Visualizing elements in the ShafarevichTate group” project:

Bibliography: dvi, ps, pdf

Mazur's comments on “visualizing elements in the
ShafarevichTate
group,”: dvi, ps, pdf

“Visualizing elements in the ShafarevichTate group,” by
Cremona and Mazur (to appear in the Journal of Experimental
Math): dvi, ps, pdf

“Visualizing elements of order three in the ShafarevichTate
group,” (to appear in the Journal of Asian
Mathematics): dvi, ps, pdf

The Mazur student project led to a preprint by William Stein
entitled “Some Abelian Varieties with Visible
ShafarevichTate
Groups.”: dvi, ps, pdf. Stein's web site also has many interesting
tables, preprints, and program related to modular forms and
modular Jacobians.


Pavlos Tzermias' lectures on “The ManinMumford Conjecture: A
Brief
Survey”: dvi, ps, pdf

Wetherell's project on “An application of the method of
Coleman and
Chabauty.”: description. It refers to Wetherell's
thesis: dvi, ps,
pdf

Cathy O'Neil's thesis (dvi, ps, pdf) on Jacobians of Curves of Genus One was the basis of Tomas Klenke's talk.

Several U of A graduates students worked with Bill McCallum on
constructing the Jacobian of a genus 1
curve. Their web site has the details. Slides for
David Marshall's talk on this
topic: dvi, ps,
pdf


Poonen's lectures at the Winter School were on background
material, but two (or more) of the papers
on his web site are relelvant to the topic:

“Algebraic families of nonzero elements of
ShafarevichTate groups”, with
ColliotThélène: pdf

“Computational aspects of curves of genus at least
2”: ps, pdf

“The MordellWeil group of a genus 2
Jacobian”: project description


Three papers related to Rubin's lectures:

“Elliptic curves with complex
multiplication”: dvi, ps, pdf

“Euler systems and modular elliptic
curves”: dvi, ps, pdf

“General Euler
systems”: dvi, ps, pdf

Karl's web site has other preprints that may be of interest.

“TateShafarevich groups of twists on an elliptic
curve”: project description


“Rational points on conics.”:
project description,
suggested readings

Cremona's web site has a number of preprints
and and slides related to his talk at the Winter School, and to
his student project. It also contains a lots of information about
symbolic computation packages, other software, and mathematics.