Jul 8, 2020
The motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$ and its action on the fundamental group of $\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$
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In this paper we introduce confluence relations for motivic Euler sums (also
called alternating multiple zeta values) and show that all linear relations
among motivic Euler sums are exhausted by our confluence relations. This
determines all automorphisms of the de Rham fundamental torsor of
$\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$ coming from the action of the
motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$. Moreover, we
also discuss other applications of our confluence relations such as an explicit
$\mathbb{Q}$-linear expansion of a given motivic Euler sum by their basis and
$2$-adic integrality of the coefficients in the expansion.
called alternating multiple zeta values) and show that all linear relations
among motivic Euler sums are exhausted by our confluence relations. This
determines all automorphisms of the de Rham fundamental torsor of
$\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$ coming from the action of the
motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$. Moreover, we
also discuss other applications of our confluence relations such as an explicit
$\mathbb{Q}$-linear expansion of a given motivic Euler sum by their basis and
$2$-adic integrality of the coefficients in the expansion.
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- arXiv ID : arXiv:2007.04288