Congruences Between Motives and Congruences Between Special Values of L-functions

来源 :第二届中法算术代数几何会议(SFCAG 2016) | 被引量 : 0次 | 上传用户:shiyiliang
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  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 spe-cial 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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