Galois theory for motivic cyclotomic multiple zeta values
Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017
Location: SLMath: Eisenbud Auditorium
Galois theory
Galois orbits
Periods
multiple zeta values
roots of unity
shuffle product
iterated integrals
motivic integration
weight spaces of modular forms
cohomology comparison isomorphisms
Lefschetz motive
cyclotomic fields
Hopf algebras
motivic periods
motivic fundamental group
14D24 - Geometric Langlands program (algebro-geometric aspects) [See also 22E57]
18M85 - Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads
14F40 - de Rham cohomology and algebraic geometry [See also 14C30, 32C35, 32L10]
11S80 - Other analytic theory (analogues of beta and gamma functions, $p$p-adic integration, etc.)
Glanois
Cyclotomic multiple zeta values (CMZV), are an interesting first bunch of examples of periods and a fruitful recent approach is to look at their motivic version (MCMZV), which are motivic periods of the fundamental groupoid of ℙ1 ∖ {0, μN, ∞}. Notably, MCMZV have a Hopf comodule structure, dual of the action of the motivic Galois group on these specific motivic periods; the explicit combinatorial formula of the coaction (Goncharov, Brown) enables, via the period map (isomorphism under Grothendieck’s period conjecture), to deduce results on CMZV. We will here highlight how to apply some Galois descents ideas to the study of these motivic periods and look at how periods of the fundamental groupoid of ℙ1 ∖ {0, μN', ∞} are embedded into periods of π1(ℙ1 ∖ {0, μN, ∞}), when N′ | N, via a few examples
Glanois.Notes
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Glanois
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