Bibliography

Bibliography [Ahl79]

L. Ahlfors, Introduction to the Theory of Analytic Functions of One Complex Variable, 3rd ed., Inter. Series in Pure and Applied Math., McGraw-Hill, All over, 1979. [An02] Y. Andr´e, Period mappings and differential equations: from C to Cp MSJ memoirs, Japanese mathematical society (ed.: M. Kashiwara (Kyoto)), 2003. [AnIh88] G. Anderson and Y. Ihara, Pro- branched coverings of P1 and higher circular -units, Annals of Math. 128 (1988), 271–293. [Apo57] T. Apostol, Mathematical Analysis, 3rd ed., Addison-Wesley Mathematics Series, Addison-Wesley, Reading, Mass., 1957. ´ Goursat, Th´ [AG1895] P. Appell and E. eorie des Fonctions Alg´ ebriques et de leurs Int´ egrales, Gauthier-Villars et Cie , Paris, 1895, with a revised edition by P. Fatou, 1929. [Ar25] , Theorie der Zopfe, Abh. Math, Hamburg Univ. 4 (1925), 47–72. [Ar47] , Theory of braids, Annals of Math. 48 (1947), 101–126. [At57] M. Atiyah, Complex analytic connections in fiber bundles, TAMS 85 (1957), 181-207. [BFr02] P. Bailey and M. Fried, Hurwitz monodromy, spin separation and higher levels of a Modular Tower, in Proceedings of Symposia in Pure Mathematics 70 (2002) editors M. Fried and Y. Ihara, 1999 von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra, August 16-27, 1999 MSRI, 79–221. [Be79] G.V. Belyi, On Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 267-276 (Russian) English Translation (1980) 247–256. [Ben91] D.J. Benson, I: Basic representation theory of finite groups and associative algebras, Cambridge Studies in advanced math., vol. 30, Cambridge U. Press, Cambridge, 1991. [BF82] R. Biggers and M. Fried, Moduli spaces of covers and the Hurwitz monodromy group, Crelles Journal 335 (1982), 87–121. [BL92] H. Lange and C. Birkenake, Complex Abelian Varieties, Springer Verlag, 1992. [Bi75] J. Birman, Braids, links and mapping class groups, Based on notes of J. Cannon: Princeton U. Press 82, 1975. [Boh47] F. Bohnenblust, The algebraical braid group, Ann. of Math. (2) 48 (1947), 127–136. [Bo86] W. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd Edition, 120 in Pure and Applied Math., Academic Press, 1986. ´ ´ [BAD62] R. Bourgne and J.-P. Azra, Ecrits et M´ emoires Math´ ematique d’ Evariste Galois, pref´ ace J. Dieudonn´e, Gauthier-Villars et Cie , Paris, Imprimeur-Editeur-Libraire, 1962. [BB1856] C.A. Briot and J.C. Bouquet, Th´ eorie des fonctions doublement p´ eriodiques et, en particular, des fonctions elliptiques, 1st Edition 1859, 2nd edition 1875, Mallet-Bachelier, Paris, 1859, with a German edition in 1862. [Ch47] W. Chow, On the algebraical braid group, Annals Math. 48 (1947), 127–136. [Cl1872] Zur theorie der Riemann’schen Flache, Math. Ann. 6 (1872), 216–230. [CTT98] R. Coleman, A. Tamagawa and P. Tzermias, The cuspidal torsion packet on the Fermat curve, J. reine angew. 496 (1998), 73–81. [Con78] J. B. Conway, Functions of One Complex Variable, 2nd ed., Grad. Texts in Math. 11 Springer-Verlag, NY, Heidelberg, Berlin, 1978. [C89] R. Courant, Methods of Mathematical Physics, II, Partial Differential Equations, Interscience Publishers, Wiley, 1989. [CG95] J.-M. Couveignes and L. Granboulan, Dessins from a geometric point of view. [DFr90] P. D` ebes and M. Fried, Rigidity and real residue class fields, Acta Arith, 56 (1990), 13–45. [DFr99] P. D` ebes and M. Fried, Integral specialization of families of rational functions, PJM (1999), To appear June 1999. 227

228

[De89]

BIBLIOGRAPHY

P. Deligne, Le group fondamental de la droute projective moins trois points, Publ. MSRI 16, Springer-Verlag, Heidelberg, New York (1989), 79–298. [Di96] Dixon and Mortimer, Permutation Groups Graduate Texts in Mathematics 163 Springer-Verlag, 1996. [DVo98] M. Dettweiler and H. V¨ olklein, Rigid tuples in Chevalley groups (1998), preprint, April 1998. [Du54] A. Durant and W. Durant, The Age of Reason, Simon and Schuster, 1954. [Fal83] G. Faltings, Endlichkeitss¨ atze u ¨ber Zahlk¨ orpern, Invent. Math. 73 (1983), 349–366. [FaKr90] H. Farkas and I. Kra, Riemann Surfaces, Graduate texts in Mathematics 71, Springer, 1980. [FKVo98] G. Frey, E. Kani and H. V¨ olklein, Curves with infinite K-rational geometric fundamental group, in: Aspects of Galois Theory, edts. H. Voelklein et. al., London Math. Soc. Lecture Notes 256, Cambridge Univ. Press (1999), 85–118. [Fr78] M.D. Fried, Galois groups and Complex Multiplication, Trans.A.M.S. 235 (1978), 141– 162. [FJ78] M.D. Fried and M. Jarden, Diophantine Properties of Subfields of Q, Amer. J. Math. 100 (1978), 653–666. [FJ86] M.D. Fried and M. Jarden, Field arithmetic, Ergebnisse der Mathematik III, vol. 11, Springer Verlag, Heidelberg, 1986. [FV91] M. Fried and H. V¨ olklein, The inverse Galois problem and rational points on moduli spaces , Math. Annalen 290 (1991), 771–800. [FrV92] M.D. Fried and H. V¨ olklein, The embedding problem over an Hilbertian-PAC field, Annals of Math 135 (1992), 469–481. [Fri70] M. Fried, On a conjecture of Schur, Mich. Math. J. 17 (1970), 41–55. [Fri73] M. Fried, The field of definition of function fields and a problem in the reducibility of polynomials in two variables, Ill. J. of Math. 17 (1973), 128–146. [Fri77] M. Fried, Fields of definition of function fields and Hurwitz families and groups as Galois groups, Communications in Algebra 5 (1977), 17–82. [Fri78] M. Fried, Galois groups and Complex Multiplication, Trans.A.M.S. 235 (1978) 141– 162. [Fri89] M. Fried, Combinatorial computation of moduli dimension of Nielsen classes of covers, Cont. Math., vol. 89, pp. 61–79, AMS, Providence, RI, 1989. [Fri90] M. Fried, Arithmetic of 3 and 4 branch point covers: A bridge provided by noncongruence subgroups of SL2 (Z), Progress in Math. Birkhauser 81 (1990), 77–117. [Fri94] M.D. Fried, review—Topics in Galois Theory, J.-P. Serre, BAMS, 1992, Bartlett and Jones Publishers, ISBN 0-86720-210-6, 30 #1 (1994), 124–135. [Fri95a] M.D. Fried, Introduction to Modular Towers: Generalizing the relation between dihedral groups and modular curves, Proceedings AMS-NSF Summer Conference, Cont. Math series, Recent Developments in the Inverse Galois Problem, 186 (1995), 111–171. [Fri95b] M. Fried, Extension of constants, rigidity, and the Chowla-Zassenhaus conjecture, Finite Fields and their applications; Carlitz Volume 1 (1995), 326–359. [Fri95c] M. Fried, Enhanced review: Serre’s Topics in Galois Theory, Proceedings of the Recent developments in the Inverse Galois Problem conferenc, AMS Cont. Math. 186 (1995), 15–32. [Fri96] M.D. Fried, Alternating groups and lifting invariants, Preprint as of 07/01/96 (1996), 1–34. [FrK97] M.D. Fried and Y. Kopeliovic, Applying Modular Towers to the inverse Galois problem, Geometric Galois Actions II Dessins d’Enfants, Mapping Class Groups and Moduli, vol. 243, Cambridge U. Press, 1997, London Mathematical Society Lecture Note series, pp. 172–197. [FKK01] M. Fried, E. Klassen, Y. Kopeliovic, Realizing alternating groups as monodromy groups of genus one covers, PAMS 129 (2000), 111–119. [Fri99] M.D. Fried, Separated variables polynomials and moduli spaces, Number Theory in Progress (Berlin-New York) (J. Urbanowicz K. Gyory, H. Iwaniec, ed.), Walter de Gruyter, 1999, Proceedings of the Schinzel Festschrift, Summer 1997, pp. 1–56. [Fr02] M.D. Fried, Moduli of relatively nilpotent extensions, Institute of Mathematical Science Analysis 1267, June 2002, Communications in Arithmetic Fundamental Groups, 70–94.

BIBLIOGRAPHY

[FH91] [Fu69] [Gr70] [GR78] [Gun66] [Gun67] [Gun67] [GN95] [Ha63] [Har77] [He62] [He66] [Hil62] [Hi65] [Hit00] [Hu1891] [Ihar86] [Ihar00]

[Ihar91]

[IhMa95]

[IhNa97] [Isa94] [Jac85] [Iha86] [Iha91] [IM95]

[KMS66] [Ka96] [K72] [Lam98] [Lan58]

229

W. Fulton and J. Harris, Representation Theory, Graduate Texts 129, 1991. W. Fulton, Hurwitz schemes and irreducibility of moduli of algebraic curves, Ann. Math. 90 (1969), 542–575. P. Griffiths, Periods of integrals of algebraic manifolds: Summary of main results and open problems, BAMS 76 #2, 228–296. B. Gross and D. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201–224. R. C. Gunning, Lectures on Riemann Surfaces, Princeton Mathematical Notes, Princeton NJ Press, 1966. R. C. Gunning, Lectures on Vector Bundles over a Riemann Surface, Princeton Mathematical Notes, Princeton NJ Press, 1967. R. C. Gunning, Special coordinate covering of Riemann surfaces, Math. Ann. 170 (1967), 67–86. R. M. Guralnick and M. G. Neubauer, Monodromy groups of branched covers: . . . , Recent dev. in IGP, vol. 186, AMS, 1995, Cont. Math, pp. 325–352. M. Hall, The theory of groups, Macmillan, 1963. R. Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, 1977. M. Heins, Selected topics in the classical theory of functions in one complex variable, Holt, Rinehart and Winston, New York, 1962. M. Heins, Complex function theory, Academic Press, New York, 1966. E. Hille, Analytic function theory, Vol. II, Introductions to higher mathematics, Ginn and Co., 1962. N. Hicks, Notes on Differential Geometry 3, Mathematical Studies, Van Nostrand, 1965. N. Hitchen, What is a Gerbe?, Notices AMS50 #2, (2003), 218–219. ¨ Uber Riemann’sche Flachen mit gebeben Verzweigungspunkten, Math. Ann. 39 (1891), 1–61. [Ar25], [Ar47], [Bi75], [Boh47], [Cl1872], [Hu1891] Y. Ihara, Profinite Braid Groups, Annals of Math. 123 (1986), 43–106. Y. Ihara, Shimura curves over finite fields and their rational points, Proceedings AMSNSF Summer Conference, 1997, Cont. Math series, Curves over finite fields, ?? (2000), ??. Y. Ihara, Braids, Galois groups and some arithmetic functions, Proceedings of the International Congress of Mathematicians, Kyoto 1990, Springer-Verlag (1991), 99– 120. Y. Ihara and M. Matsumoto, On Galois actions on profinite completions of braid groups, Proceedings AMS-NSF Summer Conference, Cont. Math series, Recent Developments in the Inverse Galois Problem 186 (1995), 173–200. Y. Ihara and H. Nakamura, On deformation of maximally degenerate stable marked curves and Oda’s problem, J. Reine. Angew. Math 487 (1997), 125–151. I. M. Isaacs, Algebra, a graduate course, 1st ed., Brooks/Cole, Pacific Grove, California, 1994. N. Jacobson, Basic Algebra I, 2nd ed., W. H. Freeman, 1985. Y. Ihara, Profinite braid groups, Annals of Math. 123 (1986), 43–106. Y. Ihara, Braids, Galois groups and some arithmetic functions, Proceedings of the International Congress, vol. Kyoto 1990, pp. 99–120, Springer-Verlag, Tokyo, 1991. Y. Ihara and M. Matsumoto, On Galois actions on profinite completions of braid groups, Proceedings AMS-NSF Summer Conference, vol. 186, 1995, Cont. Math series, Recent Developments in the Inverse Galois Problem, 173–200. A. Karrass, W. Magnus and D. Solitar, Combinatorial group theory, Interscience Publishers, J. Wiley and Sons, 1966. N. Katz, Rigid local systems, Princeton University Press 1996. I. Kra, Automorphic forms and Kleinian groups, WA Benjamin, 1972. T. Y. Lam, Representations of Finite Groups: A Hundred Years, Part I, Notices of the AMS 45 No. 3 (1998), 368–372. S. Lang, Introduction to Algebraic Geometry, Interscience tracts 5, Interscience Publishers, New York, 1958.

230

[Lan59] [LN73] [Lan71] [Ma34] [Mar45] [MM95] [MP93] [Moc96] [Ma67] [M¨ ul95]

[Moc96] [Mu66] [Mu72] [Mum76] [Na98] [Ne81] [Ra00] [Ri1851] [Ri1876] [Rig96] [R77] [Rud76] [Sch70] [Scho86] [Schr02] [Sc1890] [Se59] [Se68]

[Se72] [Ser86] [Ser90b] [Sa97] [Ser90a]

BIBLIOGRAPHY

S. Lang, Abelian Varieties, Interscience tracts 7, Interscience Publishers, New York, 1959. H. Lausch and W. Nobauer, Algebra of Polynomials, North Holland Press, 1973. S. Lang, Algebra, 4th ed., Mathematics, Addison-Wesley, 1971. ¨ W. Magnus, Uber Automorphismen von Fundamentalgruppen berandeter Fl¨ achen, Math. Ann. 109, 1934, 617–646. A. Markoff, Foundations of the algebraic theory of tresses, Trav. Inst. Math. Steklov, vol. 16, Steklov, Moscow, 1945. G. Malle and B.H. Matzat, Inverse Galois Theory, Completed as of Fall 1995. R.J. Milgra and R.C. Penner, Riemanns Moduli Space and Symmetric Groups, Cont. Math. 150 (1993), 247–290. S. Mochizuki, A theory of ordinary p-adic curves, Publ. RIMS, 32 #6 (1996), 9571151. W.S. Massey, Algebraic Topology; an introduction, Harcourt, Brace and World, New York, 1967. P. M¨ uller, Primitive monodromy groups of polynomials, Proceedings of the Recent developments in the Inverse Galois Problem conference, vol. 186, 1995, AMS Cont. Math series, pp. 385–401. S. Mochizuki, A theory of ordinary p-adic curves, Publ. RIMS, 32 #6 (1996), 9571151. D. Mumford, Introduction to Algebraic Geometry; The Red Book, Harvard Lecture Notes, 1966. D. Mumford, An analytic construction of degenerating curves over complete local rings, Comp. Math. 24 (1972), 129–174. D. Mumford, Curves and their Jacobians, Ann Arbor Lectures, Ann Arbor Press, 1976. H. Nakamura, Tangential base points and Eisenstein series, Preprint, Fall 1998, (1998). E. Neuenschwanden, Studies in the history of complex function theory II: Interactions among the French school, Riemann and Weierstrass, BAMS 5 (1981), 87–105. U. Ray, Generalized Kac-Moody algebras and some related topics, BAMS 38 #1 (2000), 1–42. B. Riemann, Grundlgen f¨ ur eine allgemeine Theorie der Functionen einer ver¨ anderlichen complexen Gr¨ osse, inaugural dissertation, G¨ ottingen, 1851. B. Riemann, Mathematische Werke, Teubner, Leipzig, 1876. L.T. Rigatelli, Evariste Galois: 1811-1832, Vita Mathematica, Vol. 11, Birkh¨ auser, 1996. D. Rohrlich, Points at infinity on the Fermat curves, Invent. Math. 39 (1977), 95–127. W. Rudin, Principles of Mathematical Analysis, 3rd ed., Inter. Series in Pure and Applied Math., McGraw-Hill, All over, 1976. A. Schinzel, Reducibility of polynomials, Actes Cong. Intern. Math. 1 (1970), 491–496. A. Scholl, Fourier coefficients of Eisenstein series on noncongruence subgroups, Math. Proc. Camb. Phil. Soc. 99 (1986), 11–17. S. Schr¨ oer, Curves with only triple ramification, preprint available from http://www.arxiv.org/PS cache/math/pdf/0206/0206091.pdf as of June 2002. H.A. Schwarz, Gesammelte Mathematische Abhandlungen, Vol. II, Verlag von Springer, Berlin, 1890. J.-P. Serre, Groups Alg´ ebriques et Corps de Classes, Hermann (1959). J.-P. Serre, Abelian -adic Representations and Elliptic Curves, McGill University Lecture Notes, Benjamin, New York • Amsterdam 1st (1968), in collaboration with Willem Kuyk and John Labute. J.-P. Serre, Propri´ et´ es galoisiennes des points d’ordre fini des courbes elliptiques, Inv. Math., 15 (1972), 259–331. J.-P. Serre, Lectures at Cal Tech, zeroxed notes, (1986) and (1997). J.-P. Serre, Revˆ etements a ramification impaire et thˆ eta-caract´ eristiques, C. R. Acad. Sci. Paris 311 (1990), 547–552. M. Sa¨idi, Revˆ etements mod´ er´ es et groupe fondamental de graphe de groupes, Compositio Math. 107 (1997), 319–338. ˜n , C. R. Acad. Sci. Paris 311 (1990), 477–482. J.-P. Serre, Relˆ evements dans A

BIBLIOGRAPHY

[Se92] [Si29] [Spr57]

[V¨ o96] [Wa79] [Wae48] [We38] [Wel69]

[Wey55]

231

J.-P. Serre, Topics in Galois Theory, Bartlett and Jones Publishers (1992), Notes by Henri Darmon, ISBN #0-86720-210-6. ¨ C.L. Siegel, Uber einige Anwendungen diophantischer Approximationen, Abh. Pr. Akad. Wiss. 1 (1929), 41–69. G. Springer, Introduction to Riemann Surfaces, 1st ed., Addison-Wesley Mathematics Series, vol. 11, Addison-Wesley, Reading, Mass., 1957. bibitem[Turn95]Turn G. Turnwald, On Schur’s conjecture, J. Austral. Math Soc. Ser. A 58 (1995), 312–357. H. V¨ olklein, Groups as Galois Groups 53, Cambridge Studies in Advanced Mathematics, Camb. U. Press, Camb. England (1996), M. Waldschmidt, Nombres Transcendental et groups algebriques, Ast´ erisque (1979), 69–70. B.L. van der Waerden, Free products of groups, Amer. J. Math. 70 (1948), 527–8. A. Weil, G´ en´ eralization des fonctions ab´eliennes, J. Math. Pure App. 17 (1938), 37–87. C. Wells (with the aid of W. Nobauer), Bibliography of literature on representable mappings of an algebraic structure into itself, Dept. of Math. Case-Western Reserve, 1969. H. Weyl, Die Idee der Riemannschen Fl¨ ache, Third Edition, B. G. Teubner, Stuttgart, 1955.