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

Joint IAS/Princeton University Number Theory Seminar
Topic:Congruences between motives and congruences between values of $L$-functions
Speaker:Olivier Fouquet
Affiliation:Université Paris-Sud
Date:Thursday, April 13
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/puias/2017/0413-OlivierFouquet

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).