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I give a global cohomological formula for the central value of the L-function of a symplectic representation on a curve up to squares and link this to arithmetic Chern-Simons theory.
I will highlight the role that Reidemeister torsion plays in that arithmetic picture, and give some results both in the topological and geometric setting.
Vasily Golyshev, Vladimir Rubtsov, Ilia Gaiur