|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||Congruences between motives and congruences between values of $L$-functions|
|Date:||Thursday, April 13|
|Time/Room:||4:30pm - 5:30pm/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).