Recent results in the theory of constant reductions
Journal de théorie des nombres de Bordeaux, Tome 3 (1991) no. 2, pp. 275-310. 
@article{JTNB_1991__3_2_275_0,
     author = {Barry Green},
     title = {Recent results in the theory of constant reductions},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {275--310},
     publisher = {Universit\'e Bordeaux I},
     volume = {3},
     number = {2},
     year = {1991},
     zbl = {0772.12004},
     mrnumber = {1149799},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1991__3_2_275_0/}
}
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Barry Green. Recent results in the theory of constant reductions. Journal de théorie des nombres de Bordeaux, Tome 3 (1991) no. 2, pp. 275-310. https://jtnb.centre-mersenne.org/item/JTNB_1991__3_2_275_0/

[A-P-Z] V. Alexandru, N. Popescu, A. Zaharescu, A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ. 28 (1989), 579-592. | Zbl

[A-W] M. Artin, G. Winters, Degenerate fibres and stable reduction of curves, Topology 10 (1971), 373-383. | MR | Zbl

[B-L] S. Bosch, W. Lütkebohmert, Stable Reduction and Uniformization of Abelian Varieties I, Math. Ann. 270 (1985), 349-379. | EuDML | MR | Zbl

[B-L-R] S. Bosch, W. Lütkebohmert, M. Raynaud, Néron Models, Mathematische Ergebnisse 21, Springer Verlag (1990). | MR | Zbl

[C-R] D. Cantor, P. Roquette, On diophantine equations over the ring of all algebraic integers, J. Number Theory 18 (1984), 1-26 | MR | Zbl

[C] C. Chevalley, Introduction to the theory of algebraic functions of one variable, A.M.S. Math. Surveys IV, 1951. | MR | Zbl

[C-K] C.C. Chang, H.J. Keisler, Model Theory, Amsterdam -London 1973. | Zbl

[D-M] P. Deligne, D. Mumford, The irreducibility of space curves of given genus, Publ. Math. IHES 36 (1969), 75-109. | EuDML | Numdam | MR | Zbl

[D1] M. Deuring, Reduktion algebraischer Funktionenkörper nach Prim-divisoren des Konstantenkörpers, Math. Z. 47 (1942), 643-654. | EuDML | JFM | MR | Zbl

[D2] M. Deuring, Die Zetafunktion einer algebraischen Kurve vom Geschlecht 1, Nachr. Akad. Wiss. Göttingen Math.-Phys.-Chem. Kl., (1955), 13-42. | MR | Zbl

[vdD] L. Van Den Dries, Elimination theory for the ring of algebraic integers, J. reine angew. Math. 388 (1988), 189-205. | MR | Zbl

[vdD-McT] L. Van Den Dries, A. Macintyre, The logic of Rumely's local-global principle, J. reine angew. Math. 407 (1990), 33-56. | MR | Zbl

[E] H.P. Epp, Eliminating wild ramification, Invent. Math. 19 (1973), 235-249. | MR | Zbl

[F-M] J. Fresnel, M. Matignon, Sur les espaces analytiques quasi-compacts de dimension 1 sur un corps valué complet ultramétrique, Annali di Matematica pura ed applicata (IV), Vol CXLV (1986), 159-210. | MR | Zbl

[G-vdP] L. Gerritzen, M. Van Der Put, Schottky groups and Mumford curves, LNM 817, Springer Verlag (1980). | MR | Zbl

[Gr-Re] H. Grauert, R. Remmert, Über die Metode der diskret bewerteten Ringe in der nicht archimedischen Analysis, Invent. Math. t. 2 (1966), 87-133. | MR | Zbl

[G-M-P 1] B.W. Green, M. Matignon, F. Pop, On valued function fields I, Manuscripta Math. 65 (1989), 257-276. | MR | Zbl

[G-M-P 2] B.W. Green, M. Matignon, F. Pop, On valued function fields II, Regular functions and elements with the uniqueness property, J. reine angew. Math. 412 (1990), 128-149. | MR | Zbl

[G-M-P 3] B.W. Green, M. Matignon, F. Pop, On valued function fields III, Reductions of algebraic curves, manuscript 1991. | Zbl

[Ka] E. Kani, The stable reduction theorem via moduli theory, Appendix to [G-M-P 3], manuscript 1991.

[Kä] T. Kässer, Reduktion von Differentialen algebraischer Funktionenkörper, Diplomarbeit, Universität Heidelberg, 1990.

[Kn] H. Knaf, Reduktion von Funktionenkörpern und Automorphismengruppen, Diplomarbeit, Universität Heidelberg, 1990.

[K] F.V. Kuhlmann, Henselian function fields, Dissertation, Heidelberg 1990. | Zbl

[L] E. Lamprecht, Restabbildungen von Divisoren I, Arch. Math. 8 (1957), 233-264. | MR | Zbl

[Ma] H. Mathieu, Das Verhalten des Geschlechts bei Konstantenreduktionen algebraischer Funktionenkörper, Arch. Math. 20 (1969), 597- 611. | MR | Zbl

[M1] M. Matignon, Thèse, Université de Bordeaux1, 1987.

[M2] M. Matignon, Genre et genre résiduel des corps de fonctions valués, Manuscripta Math. 58 (1987), 179-214. | Zbl

[M3] M. Matignon, Corps de fonctions valúes, manuscript, April 1988.

[M-O 1] M. Matignon, J. Ohm, A structure theorem for simple transcendental extensions of valued fields, Proc. Amer. Math. Soc. 104 (1988), 392-402. | MR | Zbl

[M-O 2] M. Matignon, J. Ohm, Simple transcendental extensions of valued fields III: The uniqueness property, to appear in J . Math. Kyoto Univ. | MR | Zbl

[M-B 1] L. Moret-Bailly, Groupes de Picard et problèmes de Skolem I, Ann. scient. Éc. Norm. Sup. 22 (1989), 161-179. | Numdam | MR | Zbl

[M-B 2] L. Moret-Bailly, Groupes de Picard et problèmes de Skolem II, Ann. scient. Éc. Norm. Sup. 22 (1989), 181-194. | Numdam | MR | Zbl

[N1] J. Neukirch, Kennzeichnung der p-adischen und endlichen algebraischen Zahlkörper, Invent. math. 6 (1969), 269-314. | MR | Zbl

[N2] J. Neukirch, Kennzeichnung der endlich-algebraischen Zahlkörper durch die Galoisgruppe der maximal auflösbaren Erweiterungen, J. reine angew. Math. 238 (1969), 135-147. | MR | Zbl

[O1] J. Ohm, Simple transcendental extensions of valued fields, J. Math. Kyoto Univ. 22 (1982), 201-221. | MR | Zbl

[O2 J. Ohm, Simple transcendental extensions of valued fields, II: A fundamental inequality, J. Math. Kyoto Univ. 25 (1985), 583-596. | MR | Zbl

[03] J. Ohm, The henselian defect for valued function fields, Proc. Amer. Math. Soc. 107 (1989), 299-308. | MR | Zbl

[Po] M. Polzin, Prolongement de la valeur absolue de Gauss et probleme de Skolem, Bull. Soc. math. France 116 (1988), 103-132. | Numdam | MR | Zbl

[P1] F. Pop, Galoissche Kennzeichnung p-adisch abgeschlossener Körper, J. reine angew. Math. 392 (1988), 145-175. | MR | Zbl

[P2] F. Pop, On the Galois Theory of function fields of one variable over number fields, J. reine angew. Math. 406 (1990), 200-218. | MR | Zbl

[P3] F. Pop, Isomorphisms of stratified absolute Galois groups, Habilitationsschrift, Universität Heidelberg, 1990.

[P4] F. Pop, Fields of totally Σ-adic numbers, manuscript, 1990.

[vdP] M. Van Der Put, Stable reductions of algebraic curves, Indag. Math. 46 (1984), 461-478. | MR | Zbl

[Rob] A. Robinson, Complete theories, North Holland (1956). | MR | Zbl

[R1] P. Roquette, Zur Theorie der Konstantenreduktion algebraischer Mannigfaltigkeiten, J. reine angew. Math. 200 (1958), 1-44. | MR | Zbl

[R2] P. Roquette, Solving diophantine equations over the ring of all algebraic integers, Atas de 8e Escola de Algebra, Vol 2, IMPA 84.

[R3] P. Roquette, Some tendencies in contemporary algebra, Perspectives in Mathematics, Anniversary of Oberwolfach 1984, Basel 1984, 393-422. | MR | Zbl

[R4] P. Roquette, Reciprocity in valued function fields, J. reine angew. Math. 375/376 (1987), 238-258. | MR | Zbl

[R5] P. Roquette, Über die algebraisch-zahlentheoretischen Arbeiten von Max Deuring, DMV Jahresbericht 91 Band Heft 3 (1989), 109-125. | MR | Zbl

[R6] P. Roquette, On Rumely's Local Global Principle, manuscript 1990.

[Ros] M. Rosenlicht, Equivalence relations on algebraic curves, Ann. of Math. 56 (1952), 169-191. | MR | Zbl

[Ru1] R. Rumely, Arithmetic over the ring of all algebraic integers, J. reine angew. Math. 368 (1986), 127-133. | MR | Zbl

[Ru2] R. Rumely, Capacity theory on algebraic curves, Springer L.N.M. 1378, Berlin Heidelberg New-York 1989. | MR | Zbl

[U] K. Uchida, Isomorphisms of Galois groups of algebraic function fields, Ann. of Math. 106 (1977), 589-598. | MR | Zbl

[Y] T. Youssefi, Revêtements des courbes algébriques et réductions, Thèse, Université de Bordeaux1, 1990.