36 research outputs found
Profinite completions of Burnside-type quotients of surface groups
Using quantum representations of mapping class groups we prove that profinite
completions of Burnside-type surface group quotients are not virtually
prosolvable, in general. Further, we construct infinitely many finite simple
characteristic quotients of surface groups.Comment: revised version, 17
Elliptic multizetas and the elliptic double shuffle relations
We define an elliptic generating series whose coefficients, the elliptic
multizetas, are related to the elliptic analogues of multiple zeta values
introduced by Enriquez as the coefficients of his elliptic associator; both
sets of coefficients lie in , the ring of functions
on the Poincar\'e upper half-plane . The elliptic multizetas
generate a -algebra which is an elliptic analogue of
the algebra of multiple zeta values. Working modulo , we show that the
algebra decomposes into a geometric and an arithmetic part and
study the precise relationship between the elliptic generating series and the
elliptic associator defined by Enriquez. We show that the elliptic multizetas
satisfy a double shuffle type family of algebraic relations similar to the
double shuffle relations satisfied by multiple zeta values. We prove that these
elliptic double shuffle relations give all algebraic relations among elliptic
multizetas if (a) the classical double shuffle relations give all algebraic
relations among multiple zeta values and (b) the elliptic double shuffle Lie
algebra has a certain natural semi-direct product structure analogous to that
established by Enriquez for the elliptic Grothendieck-Teichm\"uller Lie
algebra.Comment: major revision, to appear in: Int. Math. Res. No
MODULES DE DRINFELD QUASICRISTALLINS
Dans cet article nous développons la notion de module de Drinfeld quasicristallin, que l'on peut voir comme un analogue en caractéristique zéro des modules de Drinfeld classiques. On prendra garde que l'adjectif se réfère aux quasi-cristaux (au sens de [23]), sans rapport avec la théorie cristalline initiée par A. Grothendieck