Algebraic Geometry Seminar
Please see the following for more related talks:
Upcoming Seminars:
- Wednesday, April 10, 2024, 3:15pm, Physics 119, Algebraic Geometry Seminar
A new case of the BSD conjecture and deformation of line bundles
Ziquan Yang (University of Wisconsin, Madison)
- I will talk about two results. The first is a new case of
the BSD conjecture, contained in a joint work with Hamacher and Zhao.
Namely, we prove the conjecture for elliptic curves of height 1 over a
global function field of genus 1 under a mild assumption. This is
obtained by specializing a more general theorem on the Tate
conjecture. The key geometric idea is an application of rigidity
properties of the variations of Hodge structures to study deformation
of line bundles in positive and mixed characteristic. Then I will talk
about a generalization of such deformation results recently obtained
with Urbanik. Namely, we show that for a sufficiently big arithmetic
family of smooth projective varieties, there is an open dense
subscheme of the base over which all line bundles in positive
characteristics can be obtained by specializing those in
characteristic 0.
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