On the combinatorial anabelian geometry of nodally nondegenerate outer representations

DOI10.32917/hmj/1323700038zbMath1264.14041OpenAlexW2140822854WikidataQ128898945 ScholiaQ128898945MaRDI QIDQ663542

Shinichi Mochizuki, Yuichiro Hoshi

Publication date: 17 February 2012

Published in: Hiroshima Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.hmj/1323700038

zbMATH Keywords

injectivityhyperbolic curveouter Galois representationcombinatorial anabelian geometrycombinatorial cuspidalizationnodally nondegeneratesemi-graph of anabelioids

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Coverings of curves, fundamental group (14H30)

Related Items (26)

On the cuspidalization problem for hyperbolic curves over finite fields ⋮ The absolute anabelian geometry of quasi-tripods ⋮ A pro-\(l\) version of the congruence subgroup problem for mapping class groups of genus one ⋮ Little survey on I/OM and its variants and their relation to (variants of) \(\widehat{GT}\) -- old \& new ⋮ The absolute Galois group acts faithfully on regular dessins and on Beauville surfaces ⋮ On the procongruence completion of the Teichmüller modular group ⋮ The Galois action on geometric lattices and the mod-\(\ell \) I/OM ⋮ A restricted Magnus property for profinite surface groups ⋮ The semi-absolute anabelian geometry of geometrically pro-\(p\) arithmetic fundamental groups of associated low-dimensional configuration spaces ⋮ On the kernels of the pro-\(l\) outer Galois representations associated to hyperbolic curves over number fields ⋮ Galois-theoretic characterization of geometric isomorphism classes of quasi-monodromically full hyperbolic curves with small numerical invariants ⋮ Finite tripod variants of I/OM. On Ihara's question/Oda-Matsumoto conjecture ⋮ Automorphisms of procongruence curve and pants complexes ⋮ On topological and combinatorial structures of pointed stable curves over algebraically closed fields of positive characteristic ⋮ Birational anabelian Grothendieck conjecture for curves over arbitrary cyclotomic extension fields of number fields ⋮ On the centralizer of the image of the universal outer monodromy representation of the moduli stack of pointed hyperbolic curves ⋮ The geometry of hyperbolic curvoids ⋮ Inter-universal Teichmüller theory. I: Construction of Hodge theaters ⋮ Difference between \(l\)-adic Galois representations and pro-\(l\) outer Galois representations associated to hyperbolic curves ⋮ On copies of the absolute Galois group in $\operatorname {Out}F_2$ ⋮ Congruence topologies on the mapping class group ⋮ Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks ⋮ Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero ⋮ Heidelberg Lectures on Fundamental Groups ⋮ On Monodromically Full Points of Configuration Spaces of Hyperbolic Curves ⋮ Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups

Cites Work

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• On the combinatorial cuspidalization of hyperbolic curves
• The congruence subgroup property for the hyperelliptic modular group: the open surface case
• Absolute anabelian cuspidalization of proper hyperbolic curves
• The algebraic and anabelian geometry of configuration spaces
• Absolute anabelian cuspidalizations of configuration spaces of proper hyperbolic curves over finite fields
• The local pro-p anabelian geometry of curves
• A combinatorial version of the Grothendieck conjecture
• Semi-graphs of anabelioids
• Braid monodromies on proper curves and pro-ℓ Galois representations
• The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$
• Mapping-class-group action versus Galois action on profinite fundamental groups

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