Abstract:

In his work on motivic multiple L-values, Deligne gave an algebraic generator for the space of motivic Euler sums. Afterwards, Glanois revisited Deligne's work and gave a Q-basis for the space of motivic Euler sums using a similar construction as Deline's, which she called "Deligne family". Their proof of Deligne family being a basis makes use of the coproduct structure equipped in the space of motivic Euler sums, which does not provide a way to compute the expression (coefficients) of a given Euler sum by that basis. In this talk I will first introduce Deligne family with slight modification, and give an explicit reduction procedure by linear relation to express Euler sums of depth two by our modified Deligne family. As a natural consequence of my reduction algorithm, we find that the modified Deligne family in fact gives a Z₂-basis rather than just a Q-basis. This is an on-going joint research work with Minoru Hirose at Kyushu University.