I understand, to some extent, Tate's thesis. Could somebody explain perhaps what are the epsilon factors in Beilinson's works, such as "$\epsilon$-factors for Gauss-Manin determinants", or "Topological $\epsilon$-factors"? How do they mimic the usual ones? Are they some categorification (since the usual one is a number, and those ones seem to be lines)? Is there some intuition for the construction in "Topological $\epsilon$-factors" or, perhaps more importantly, for the need for construction?

Edit: I also know vaguely that epsilon-factors should be also associated to Galois-side-data, and the ones in Beilinson's works mimic those, and not the "automorphic" ones from Tate's thesis.

Thank you, Sasha



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