A construction of the polylogarithm motive - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

A construction of the polylogarithm motive

Résumé

Classical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial variation. By results of Beilinson-Deligne, Huber-Wildeshaus, and Ayoub, this polylogarithm variation has a lift to the category of mixed Tate motives over $S$, whose existence is proved by computing the corresponding space of extensions in both the motivic and the Hodge settings. In this paper, we construct the polylogarithm motive as an explicit relative cohomology motive, namely that of the complement of the hypersurface $\{1-zt_1\cdots t_n=0\}$ in affine space $\mathbb{A}^n_S$ relative to the union of the hyperplanes $\{t_i=0\}$ and $\{t_i=1\}$.

Dates et versions

hal-04109369 , version 1 (30-05-2023)

Identifiants

Citer

Clément Dupont, Javier Fresán. A construction of the polylogarithm motive. 2023. ⟨hal-04109369⟩
12 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More