Upper bounds for dimensions of the spaces of p-adic multiple
zeta values
(and multiple L-values)
(Un exposé de Go Yamashita au séminaire de
théorie des nombres de Chevaleret le 27 mars 2006)
Résumé :
We show the upper bounds of p-adic multiple zeta value
(resp. L-value) spaces.
The bounds are related to algebraic K-theory.
It is the p-adic analogue of the theorem of
Goncharov, Terasoma, Deligne-Goncharov (resp. Deligne-Goncharov).
In the p-adic multiple L-value case,
the bounds are not best possible in general.
The gap between the true dimensions and the bounds related
algebraic K-theory is related to spaces of modular forms,
by the similar way as complex multiple L-values.
We also formulate the p-adic analogue of Grothendieck's
conjecture about an element of motivic Galois group of
the category of mixed Tate motives.
It seems related to "Cebotarev density" of the motivic Galois group.