Congruences between motives and congruences between values of $L$-functions

Congruences between motives and congruences between values of LL-functions - Olivier Fouquet

Olivier Fouquet
Université Paris-Sud
April 13, 2017
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).