BIRS Workshop Lecture Videos
Congruences between motives and congruences between values of \(L\)-functions Fouquet, Olivier
If two motives are congruent, is it the case that the special values of their respective \(L\)-functions are congruent, or - more precisely - can the formula predicting special values of motivic \(L\)-functions be interpolated in \(p\)-adic families of motives? I will explain how the formalism of the Weight-Monodromy filtration for \(p\)-adic families of Galois representations sheds light on this question (and suggests a perhaps surprising answer).
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