Congruences between motives and congruences between values of L-functions

Congruences between motives and congruences between values of L-functions

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Olivier Fouquet , Paris 11
IAS Room S-101

If two motives are congruent, is it the case that the special values of their respective L-functions are congruent? 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).