Multizeta values: Lie algebras and periods on $mathfrak{M} {0,n}$ - Mathematics > Number TheoryReport as inadecuate




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Abstract: This thesis is a study of algebraic and geometric relations between multizetavalues. In chapter 2, we prove a result which gives the dimension of theassociated depth-graded pieces of the double shuffle Lie algebra in depths 1and 2. In chapters 3 and 4, we study geometric relations between multizetavalues coming from their expression as periods on $\mathfrak{M} {0,n}$. The keyingredient in this study is the top dimensional de Rham cohomology of specialpartially compactified moduli spaces associated to multizeta values. In chapter3, we give an explicit expression for a basis, represented by polygons, of thiscohomology. In chapter 4, we generalize this method to explicitly describe thebases of the cohomology of other partially compactified moduli spaces. Thisthesis concludes with a result which gives a new presentation of$Pic\overline{\mathfrak{M}} {0,n}$.



Author: Sarah Carr

Source: https://arxiv.org/







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