The faithfulness of the monodromy representations associated with certain families of algebraic curves

DOI10.1016/S0022-4049(00)00056-6zbMath1045.14013OpenAlexW2073476072MaRDI QIDQ5939818

Mamoru Asada

Publication date: 21 October 2001

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(00)00056-6

zbMATH Keywords

elliptic curveGalois representationgenusalgebraic fundamental groupsfaithfulness of the monodromy representationfamily of \(n\)-pointed algebraic curves

Mathematics Subject Classification ID

Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) (14G32) Families, moduli of curves (algebraic) (14H10) Coverings of curves, fundamental group (14H30) Homotopy theory and fundamental groups in algebraic geometry (14F35)

Related Items (24)

Tamely ramified covers of the projective line with alternating and symmetric monodromy ⋮ A pro-\(l\) version of the congruence subgroup problem for mapping class groups of genus one ⋮ The congruence subgroup problem for the free metabelian group on two generators ⋮ On the index of congruence subgroups of \(\Aut(F_n)\). ⋮ On the procongruence completion of the Teichmüller modular group ⋮ On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves ⋮ Galois-theoretic characterization of geometric isomorphism classes of quasi-monodromically full hyperbolic curves with small numerical invariants ⋮ Automorphisms of procongruence curve and pants complexes ⋮ Arithmetic Veech sublattices of SL\((2,\mathbf {Z})\) ⋮ Notes on hyperelliptic mapping class groups ⋮ Nonabelian level structures, Nielsen equivalence, and Markoff triples ⋮ The congruence subgroup problem for low rank free and free metabelian groups ⋮ Galois coverings of moduli spaces of curves and loci of curves with symmetry ⋮ The congruence subgroup property for \(\Aut F_2\): a group-theoretic proof of Asada's theorem. ⋮ The level four braid group ⋮ Moduli interpretations for noncongruence modular curves ⋮ Inter-universal Teichmüller theory. I: Construction of Hodge theaters ⋮ Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups ⋮ The IA-congruence kernel of high rank free metabelian groups ⋮ The congruence subgroup problem for the free metabelian group on \(n\geq 4\) generators ⋮ Congruence topologies on the mapping class group ⋮ Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero ⋮ On Monodromically Full Points of Configuration Spaces of Hyperbolic Curves ⋮ Congruence subgroups of braid groups

Cites Work

• Pro-\(\ell\) branched coverings of \(P^ 1\) and higher circular \(\ell\)- units
• A note on ramification of the Galois representation on the fundamental group of an algebraic curve
• Correspondances modulaires et les fonctions \(\zeta\) de courbes algébriques
• Pro-\(l\) pure braid groups of Riemann surfaces and Galois representations
• Exactness properties of profinite completion functors
• On the filtration of topological and pro-\(\ell\) mapping class groups of punctured Riemann surfaces
• Torsion elements and centralizers in free products of profinite groups.
• ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
• Mapping-class-group action versus Galois action on profinite fundamental groups
• Mapping class groups and their relationship to braid groups
• Fibre Systems of Jacobian Varieties: (III. Fibre Systems of Elliptic Curves)
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