Arakelov Euler Characteristics
نویسنده
چکیده
Fröhlich suggested considering invariants of ON together with the trace pairing (x, y) → TrN/Q(xy). This leads to local and global Hermitian discriminants of (ON, Tr) in “Hermitian classgroups.” Cassou-Noguès and Taylor showed these discriminants were enough to determine both local and global symplectic root numbers. This approach will be generalized to projective schemes over Z in lecture 3. One application: Unconditional geometric proofs that various root numbers are positive, as predicted by other conjectures (Birch-Sw-Dyer).
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My primary research interests are in Number Theory and Algebraic Geometry. They often lead me into some related subjects. The research I have done so far can be separated into the following four topics. I am currently pursuing further the rst three of them. Let me now describe in some more details my contributions and research plans in the above areas. I want to note speciically that the third ...
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