10:05 - 10.55 (+ epilogue until 11.30)
Carslaw 709 on Friday 7 March
The Brauer-Manin Obstruction on Curves
When a variety violates the Hasse principle, this can
be due to an obstruction known as the Brauer-Manin obstruction.
It is an unsolved problem whether all violations of the
Hasse principle on curves are due to this obstruction.
I shall describe computations in progress which test
a wide selection of curves, and tries to test for these examples
whether the Brauer-Manin obstruction is the cause
of all violations of the Hasse principle. This has involved
the development of several new techniques, exploiting
the embedding of a curve in its Jacobians via a rational
divisor class of degree 1.