and Anabelian Geometry

October 25 Monday, 17:10--18:00 | |

M. Asada, H. Nakamura, N. Takao, H. Tsunogai;
Easy walking in GT theory and anabelian geometry, II
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In this talk we shall introduce some basic notions to understand pro-l (pro-unipotent) aspects of the title of this conference for a wider public of mathematicians including graduate students. The Galois actions on the pro-l fundamental group of algebraic curves have been an important subject to find arithmetic nature of anabelian curves since Ihara's works on in 1980's. We explain weight filtration, associated Lie algebras and derivation algebras in the case of hyperbolic curves, and generalization to configuration spaces of curves. A fundamental result concerned here is injectivity of a sequence of derivation algebras and its stability, that leads to settlement of Oda's conjecture on the common Galois factor of the universal pro-l monodromy representation. If time allows, we mention relationships of Grothendieck-Teichmüller Lie algebra, Zagier's conjecture on multiple zeta values and Ihara's stable derivation algebra. |