References AHGT

A selection of references on Anabelian Arithmetic Geometry in Arithmetic and Homotopic Galois Theory prior to 2023. For recent publications, see the AHGT publications overview.

2022

1. Galois sections and p-adic period mappings

   by

   L. Betts, and J. Stix:.

   In arXiv e-prints,

   Apr 2022

   ArXiv
2. Category-theoretic Reconstruction of Schemes from Categories of Reduced Schemes

   by

   T. Yuji.

   In RIMS Preprint,

   Mar 2022
3. Birational Anabelian Grothendieck Conjecture for Curves over Arbitrary Cyclotomic Extension Fields of Number Fields

   by

   S. Tsujimura.

   In RIMS Preprint,

   Feb 2022
4. Criteria for good reduction of hyperbolic polycurves

   by

   I. Nagamachi.

   In Math. J. Okayama Univ.,

   Feb 2022
5. Explicit Estimates in Inter-universal Teichmuller Theory

   by

   S. Mochizuki, I. Fesenko, Y. Hoshi, A. Minamide, and W. Porowski.

   In Kodai Mathematical Journal,

   Feb 2022
6. Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization

   by

   Y. Hoshi, and S. Mochizuki.

   Lecture Notes in Mathematics, Springer.

   Feb 2022
7. A note on highly Kummer-faithful fields

   by

   Y. Ozeki, and Y. Taguchi.

   In Kodai Math. J.,

   Feb 2022
8. Genus zero modular operad and absolute Galois group

   by

   N. Combe, and Y. Manin.

   In North-W. Eur. J. of Math.,

   Feb 2022
9. Anabelian geometry of certain types of hyperbolic polycurves

   by

   N. Takao.

   In J. Algebra,

   Feb 2022
10. Construction of Non-\timesμ-Indivisible TKND-AVKF-fields

    by

    S. Tsujimura.

    In Kodai Mathematical Journal,

    Feb 2022
11. Newton polygon stratification of the Torelli locus in unitary Shimura varieties

    by

    W. Li, E. Mantovan, R. Pries, and Y. Tang.

    In Int. Math. Res. Not. IMRN,

    Feb 2022

2021

1. Galois-theoretic Characterization of Geometric Isomorphism Classes of Quasi-monodromically Full Hyperbolic Curves with Small Numerical Invariants

   by

   Y. Hoshi, and Y. Iijima.

   In RIMS Preprint,

   Dec 2021
2. Homomorphisms of Global Solvably Closed Galois Groups Compatible with Cyclotomic Characters

   by

   Y. Hoshi.

   In RIMS Preprint,

   Dec 2021
3. Notes on hyperelliptic mapping class groups

   by

   M. Boggi.

   In arXiv e-prints,

   Oct 2021

   ArXiv
4. Anabelian Group-theoretic Properties of the Pro-p Absolute Galois Groups of Henselian Discrete Valuation Fields

   by

   A. Minamide, and S. Tsujimura.

   In RIMS Preprint,

   Aug 2021
5. Automorphisms of procongruence curve and pants complexes

   by

   M. Boggi, and L. Funar.

   In arXiv e-prints,

   Jul 2021

   ArXiv
6. The Action of GT-Shadows on Child’s Drawings

   by

   V. Dolgushev.

   In arXiv e-prints,

   Jun 2021

   ArXiv
7. Construction of Abundant Explicit Nongeometric Pro-p Galois Sections of Punctured Projective Lines

   by

   Y. Hoshi, and S. Tsujimura.

   In RIMS Preprint,

   Jun 2021
8. Mono-anabelian Reconstruction of Solvably Closed Galois Extensions of Number Fields

   by

   Y. Hoshi.

   In RIMS Preprint,

   May 2021
9. A theory of dormant opers on pointed stable curves – a proof of Joshi’s conjecture

   by

   Y. Wakabayashi.

   In arXiv e-prints,

   Apr 2021

   ArXiv
10. A linear variant of GT

    by

    F. Pop, and A. Topaz.

    In arXiv e-prints,

    Apr 2021

    ArXiv
11. Anabelian geometry of complete discrete valuation fields and ramification filtrations

    by

    T. Murotani.

    In RIMS Preprint,

    Mar 2021
12. A study on anabelian geometry of higher local fields

    by

    T. Murotani.

    In RIMS Preprint,

    Mar 2021
13. Mono-anabelian reconstruction of generalized fiber subgroups from a configuration space groupequipped with its collection of log-full subgroups

    by

    K. Higashiyama.

    In RIMS Preprint,

    Mar 2021
14. On the tempered fundamental groups of hyperbolic curves of genus 0 over \overline\mathbbQ_p

    by

    K. Higashiyama.

    In RIMS Preprint,

    Feb 2021
15. Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks

    by

    S. Tsujimura.

    In Kodai Math. J.,

    Feb 2021
16. Inter-universal Teichmüller theory: (I) Construction of Hodge theaters, (II) Hodge-Arakelov-theoretic evaluation, (III) Canonical splittings of the log-theta-lattice, (IV) Log-volume computations and set-theoretic foundations

    by

    S. Mochizuki.

    In Publ. Res. Inst. Math. Sci.,

    Feb 2021
17. Towards minimalistic Neukirch and Uchida theorems

    by

    F. Pop, and A. Topaz.

    In Homotopic and Geometric Galois Theory,

    Feb 2021
18. Variations of Eisenstein invariants for elliptic actions on a free profinite group

    by

    H. Nakamura.

    In ,

    Feb 2021

2020

1. Combinatorial Construction of the Absolute Galois Group of the Field of Rational Numbers

   by

   Y. Hoshi, S. Mochizuki, and S. Tsujimura.

   In RIMS Preprint,

   Dec 2020
2. Automorphisms of procongruence mapping class groups

   by

   M. Boggi.

   In arXiv e-prints,

   Nov 2020

   ArXiv
3. On the Semi-absoluteness of Isomorphisms between the Pro-p Arithmetic Fundamental Groups of Smooth Varieties over p-adic Local Fields

   by

   K. Higashiyama.

   In RIMS Preprint,

   Oct 2020
4. On Surjective Homomorphisms from a Configuration Space Group to a Surface Group

   by

   K. Sawada.

   In RIMS Preprint,

   Jul 2020
5. Combinatorial Belyi cuspidalization and arithmetic subquotients of the Grothendieck-Teichmüller group

   by

   S. Tsujimura.

   In Publ. Res. Inst. Math. Sci.,

   Jul 2020
6. A note on an anabelian open basis for a smooth variety

   by

   Y. Hoshi.

   In Tohoku Math. J. (2),

   Jul 2020
7. On the arithmetic of abelian varieties

   by

   M. Saı̈di, and A. Tamagawa.

   In J. Reine Angew. Math.,

   Jul 2020
8. Recent progress in higher-dimensional anabelian geometry

   by

   N. Takao.

   In Algebraic number theory and related topics 2016, Res. Inst. Math. Sci. (RIMS), Kyoto.

   Jul 2020
9. Belyi’s theorem in characteristic two

   by

   Y. Sugiyama, and S. Yasuda.

   In Compos. Math.,

   Jul 2020

2019

1. The m-step solvable anabelian geometry of number fields

   by

   M. Saı̈di, and A. Tamagawa.

   In arXiv e-prints,

   Sep 2019

   ArXiv
2. The automorphism groups of the profinite braid groups

   by

   A. Minamide, and H. Nakamura.

   In arXiv e-prints,

   Jul 2019

   ArXiv
3. Hurwitz Stacks of Groups Extensions and Irreducibility

   by

   B. Collas, and S. Maugeais.

   In arXiv e-prints,

   Jun 2019

   ArXiv
4. Mono-anabelian reconstruction of number fields

   by

   Y. Hoshi.

   In On the examination and further development of inter-universal Teichmüller theory, Res. Inst. Math. Sci. (RIMS), Kyoto.

   Jun 2019
5. A pro-l version of the congruence subgroup problem for mapping class groups of genus one

   by

   Y. Hoshi, and Y. Iijima.

   In J. Algebra,

   Jun 2019
6. Finite tripod variants of I/OM: on Ihara’s question/Oda-Matsumoto conjecture

   by

   F. Pop.

   In Invent. Math.,

   Jun 2019
7. Operads of genus zero curves and the Grothendieck-Teichmüller group

   by

   P. Boavida de Brito, G. Horel, and M. Robertson.

   In Geom. Topol.,

   Jun 2019

2018

1. On Galois action on stack inertia of moduli spaces of curves

   by

   B. Collas, and S. Maugeais.

   In Publ. RIMS (to appear),

   Nov 2018

   ArXiv
2. Reconstruction of Invariants of Configuration Spaces of Hyperbolic Curves from Associated Lie Algebras

   by

   K. Sawada.

   In RIMS Preprint,

   Nov 2018
3. Finiteness of Isomorphism Classes of Hyperbolic Polycurves with Prescribed Fundamental Groups

   by

   K. Sawada.

   In RIMS Preprint,

   Sep 2018
4. A p-adic Analytic Approach to the Absolute Grothendieck Conjecture

   by

   T. Murotani.

   In RIMS Preprint,

   Aug 2018
5. The Galois action on the lower central series of the fundamental group of the Fermat curve

   by

   R. Davis, R. Pries, and K. Wickelgren.

   In arXiv e-prints,

   Aug 2018

   ArXiv
6. Finite Quotients of Fundamental Groups and Moduli Spaces of Curves in Positive Characteristic

   by

   Y. Yang.

   In RIMS Preprint,

   Apr 2018
7. The Combinatorial Mono-anabelian Geometry of Curves over Algebraically Closed Fields of Characteristic p>0

   by

   Y. Yang.

   In RIMS Preprint,

   Jan 2018
8. A birational anabelian reconstruction theorem for curves over algebraically closed fields in arbitrary characteristic

   by

   M. Lüdtke.

   In Israel J. Math.,

   Jan 2018
9. A refined version of Grothendieck’s anabelian conjecture for hyperbolic curves over finite fields

   by

   M. Saidi, and A. Tamagawa.

   In J. Algebraic Geom.,

   Jan 2018
10. Sites whose topoi are the smooth representations of locally prodiscrete monoids

    by

    S. Kondo, and S. Yasuda.

    In J. Algebra,

    Jan 2018
11. The Galois action and cohomology of a relative homology group of Fermat curves

    by

    R. Davis, R. Pries, V. Stojanoska, and K. Wickelgren.

    In J. Algebra,

    Jan 2018

2017

1. On a Hom-version of the Grothendieck Conjecture for Almost Open Immersions of Curves

   by

   Y. Yang.

   In RIMS Preprint,

   Sep 2017
2. Algorithmic approach to Uchida’s theorem for one-dimensional function fields over finite fields

   by

   K. Sawada.

   In RIMS Preprint,

   Jul 2017
3. Group-theoreticity of Numerical Invariants and Distinguished Subgroups of Configuration Space Groups

   by

   Y. Hoshi, A. Minamide, and S. Mochizuki.

   In RIMS Preprint,

   Mar 2017
4. A refined version of Grothendieck’s birational anabelian conjecture for curves over finite fields

   by

   M. Saı̈di, and A. Tamagawa.

   In Adv. Math.,

   Mar 2017
5. Commuting-liftable subgroups of Galois groups II

   by

   A. Topaz.

   In J. Reine Angew. Math.,

   Mar 2017
6. Arithmetic in the fundamental group of a p-adic curve. On the p-adic section conjecture for curves

   by

   F. Pop, and J. Stix.

   In J. Reine Angew. Math.,

   Mar 2017
7. Moving frames and Eisenstein invariants

   by

   H. Nakamura.

   In Various Aspects of Multiple Zeta Values 2016, .

   Mar 2017
8. Pro-categories in homotopy theory

   by

   I. Barnea, Y. Harpaz, and G. Horel.

   In Algebr. Geom. Topol.,

   Mar 2017
9. Profinite completion of operads and the Grothendieck-Teichmüller group

   by

   G. Horel.

   In Adv. Math.,

   Mar 2017

2016

1. On profinite Eisenstein periods in the monodromy of universal elliptic curves

   by

   H. Nakamura.

   In ,

   Jan 2016
2. Anabelian geometry with étale homotopy types

   by

   A. Schmidt, and J. Stix.

   In Ann. of Math. (2),

   Jan 2016
3. A projective model structure on pro-simplicial sheaves, and the relative étale homotopy type

   by

   I. Barnea, and T. Schlank.

   In Adv. Math.,

   Jan 2016

2015

1. Topics in absolute anabelian geometry III: global reconstruction algorithms

   by

   S. Mochizuki.

   In J. Math. Sci. Univ. Tokyo,

   Jan 2015

   PrePrint
2. Composantes irréductibles de lieux spéciaux d’espaces de modules de courbes, action galoisienne en genre quelconque

   by

   B. Collas, and S. Maugeais.

   In Ann. Inst. Fourier (Grenoble),

   Jan 2015
3. On the birational section conjecture with local conditions

   by

   J. Stix.

   In Invent. Math.,

   Jan 2015

2014

1. Galois coverings of moduli spaces of curves and loci of curves with symmetry

   by

   M. Boggi.

   In Geom. Dedicata,

   Jan 2014
2. On the procongruence completion of the Teichmüller modular group

   by

   M. Boggi.

   In Trans. Amer. Math. Soc.,

   Jan 2014
3. The Grothendieck conjecture for hyperbolic polycurves of lower dimension

   by

   Y. Hoshi.

   In J. Math. Sci. Univ. Tokyo,

   Jan 2014
4. Some remarks on field towers arising from pronilpotent universal monodromy representations

   by

   N. Takao.

   In Algebraic number theory and related topics 2012, Res. Inst. Math. Sci. (RIMS), Kyoto.

   Jan 2014

2013

1. Topics surrounding the combinatorial anabelian geometry of hyperbolic curves IV: discreteness and sections

   by

   Y. Hoshi, and S. Mochizuki.

   In RIMS Preprint,

   Sep 2013
2. Resolution of nonsingularities for Mumford curves

   by

   E. Lepage.

   In Publ. Res. Inst. Math. Sci.,

   Sep 2013
3. On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves: genus zero case

   by

   Y. Hoshi.

   In Tohoku Math. J. (2),

   Sep 2013
4. Topics in absolute anabelian geometry II: decomposition groups and endomorphisms

   by

   S. Mochizuki.

   In J. Math. Sci. Univ. Tokyo,

   Sep 2013

   PrePrint
5. Birational p-adic Galois sections in higher dimensions

   by

   J. Stix.

   In Israel J. Math.,

   Sep 2013
6. On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves

   by

   H. Nakamura.

   In Publ. Res. Inst. Math. Sci.,

   Sep 2013

2012

1. Topics surrounding the combinatorial anabelian geometry of hyperbolic curves III: tripods and tempered fundamental groups

   by

   Y. Hoshi, and S. Mochizuki.

   In RIMS Preprint,

   Nov 2012
2. Action of a Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups of genus one

   by

   B. Collas.

   In Int. J. Number Theory,

   Nov 2012
3. Topics surrounding the combinatorial anabelian geometry of hyperbolic curves I: inertia groups and profinite Dehn twists

   by

   Y. Hoshi, and S. Mochizuki.

   In Galois-Teichmüller theory and arithmetic geometry, Math. Soc. Japan, Tokyo.

   Nov 2012
4. \Bbb Z/\ell abelian-by-central Galois theory of prime divisors

   by

   F. Pop.

   In The arithmetic of fundamental groups—PIA 2010, Springer, Heidelberg.

   Nov 2012
5. Braid monodromies on proper curves and pro-\ell Galois representations

   by

   N. Takao.

   In J. Inst. Math. Jussieu,

   Nov 2012
6. Descent obstruction and fundamental exact sequence

   by

   D. Harari, and J. Stix.

   In The arithmetic of fundamental groups—PIA 2010, Springer, Heidelberg.

   Nov 2012

2011

1. On the combinatorial anabelian geometry of nodally nondegenerate outer representations

   by

   Y. Hoshi, and S. Mochizuki.

   In Hiroshima Math. J.,

   Nov 2011
2. Continuous group actions on profinite spaces

   by

   G. Quick.

   In J. Pure Appl. Algebra,

   Nov 2011

2010

1. Arithmetic elliptic curves in general position

   by

   S. Mochizuki.

   In Math. J. Okayama Univ.,

   Nov 2010

   PrePrint
2. Tempered fundamental group and metric graph of a Mumford curve

   by

   E. Lepage.

   In Publ. Res. Inst. Math. Sci.,

   Nov 2010
3. Harmonic and equianharmonic equations in the Grothendieck-Teichmüller group. III

   by

   H. Nakamura, H. Tsunogai, and S. Yasuda.

   In J. Inst. Math. Jussieu,

   Nov 2010

2007

1. A combinatorial version of the Grothendieck conjecture

   by

   S. Mochizuki.

   In Tohoku Math. J. (2),

   Nov 2007
2. Absolute anabelian cuspidalizations of proper hyperbolic curves

   by

   S. Mochizuki.

   In J. Math. Kyoto Univ.,

   Nov 2007

2003

1. On a geometric description of \rmGal(\overline\bf Q_p/\bf Q_p) and a p-adic avatar of \widehatGT

   by

   Y. André.

   In Duke Math. J.,

   Nov 2003
2. Topics surrounding the anabelian geometry of hyperbolic curves

   by

   S. Mochizuki.

   In Galois groups and fundamental groups, Cambridge Univ. Press, Cambridge.

   Nov 2003

1999

1. The local pro-p anabelian geometry of curves

   by

   S. Mochizuki.

   In Invent. Math.,

   Nov 1999

1995

1. On exterior Galois representations associated with open elliptic curves

   by

   H. Nakamura.

   In J. Math. Sci. Univ. Tokyo,

   Nov 1995

1994

1. On Grothendieck’s conjecture of birational anabelian geometry

   by

   F. Pop.

   In Ann. of Math. (2),

   Nov 1994