# Special Jerusalem Mathematics Colloquium

יום שני, י באייר, תשס"ג

Monday, 12th May 2003, 2:15 pm

Mathematics Building Lecture Room 2

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On the occasion of his receiving the 2003 Wolf Prize

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John Tate

## (University of Texas)

will give a lecture entitled

"Jacobians of Plane Algebraic Curves"

** Abstract: ** This is a report on joint work with Mike Artin
and Fernando Villegas. Let *C* -> *S* be a flat family of
plane cubic curves over an arbitrary base scheme *S*, and
*J* -> *S* be the degree 0 part of the relative Picard scheme
of *C/S*. (Thus *J* is a group scheme over *S*, whose
fiber at a point, *s* in *S* where the fiber of *C* is
smooth, is the Jacobian of that fiber.) If 6 is invertible on
*S*, then *J* is described in Weierstrass form by the
classical invariants of ternary cubic forms. We give explicitly some
less invariant functions which describe *J* in generalized Weierstrass
form over an arbitrary base *S*.

Light refreshments will be served following the lecture.

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