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EXISTENTIALLY CLOSED FIELDS WITH DIFFERENCE/DIFFERENTIAL OPERATORS (Model theoretic aspects of the notion of independence and dimension)

INO, KAI 京都大学

2023.04

概要

We survey separably differentially closed fields and separable differential closure in comparison with differentially closed fields and differential closure. Also we observe several topics around the theory of separably differentially closed fields.

参考文献

[1] L. Blum Generalized algebraic structures: A model theoretic approach. Ph.D. Thesis, Massachusetts Institute of Technology, 1968.

[2] L. Blum. Differentially Closed Fields: A Model Theoretic Tour. Contributions to Algebra,

Academic Press Inc., 1977.

[3] R. Bustamante. Theorie des modeles des corps differentiellement clos avec un automorphisme

generique. PhD Thesis. Universite Paris 7, 2005.

[4] R. Bustamante Medina. Differentially closed fields of characteristic zero with a generic automorphism. Revista de Matematica: Teorfa y Aplicaciones, 14(1):81-100, 2007.

[5] Guy Casale, James Freitag, and Joel Nagloo. Ax-Lindemann-Weierstrass with derivatives and

the genus O Fuchsian groups. Annals of Mathematics, 192(3):721-765, 2020.

[6] R. Cohn. A difference-differential basis theorem. Canadian J. Math. 22, No. 6, pp.1224-1237,

1970.

[7] Z. Chatzidakis and Ehud Hrushovski. Model theory of difference fields. Trans. Amer. Math.

Soc., 351(8):2997-3071, 1999.

[8] Z. Chatzidakis, Generic automorphism of separably closed fields, Illinois Journal of Mathematics Volume 45, Number 3, Fall 2001, Pages 693-733 S 0019-2082.

75

KAI INO DEPARTMENT OF MATHEMATICS UNIVERSITY OF MANCHESTER

[9] Z. Chatzidakis, E. Hrushovski, Y. Peterzil, Model theory of difference fields, II: Periodic

ideals and the trichotomy in all characteristics, Proceedings of the London Math. Society (3)

85 (2002), 257-311.

[10] G. Cherlin, S. Shelah. Superstable fields and groups. Annals of Mathematical Logic. 18:227270, 1980.

[11] F. Delon. Ideaux et types sur les corps separablement clos. Suplemment au Bulletin de la

societe Mathematique de France. Memoire No.33, Tome 116, 1988.

[12] Matthew DeVilbiss and James Freitag. Generic differential equations are strongly minimal.

Compositio Mathematica. 2023.

[13] Y. Ershov. Fields with a solvable theory (English translation). Sov. Math. Doklady, 8:575-576,

1967.

[14] James Freitag and Thomas Scanlon. Strong minimality and the j-function. Journal of the

European Mathematical Society, 20(1):119-136, 2017.

[15] J. Gogolok. Model theory of derivations of the Frobenius map revisited. Journal of Symbolic

Logic, DOI:10.1017 /jsl.2021.85.

[16] N. Guzy and C. Riviere. On existentially closed partial differential fields with an automorphism. Preprint 2007.

[17] C. Hardouin and M. Singer. Differential Galois theory of linear difference equations. Mathematische Annalen 342(2), pp.333-377, 2008.

[18] E. Hrushovski, The Mordell-Lang conjecture for function fields, J. Amer. Math. Soc. 9 no. 3

(1996) 667-690.

[19] E. Hrushovski. The Manin-Mumford conjecture and the model theory of difference fields.

Annals of Pure and Applied Logic, 112(1), pp.43-115, 2001.

[20] K. Ino, Model theory of separably differentially closed fields. PhD Thesis, The University of

Manchseter, 2023.

[21] K. Ino, 0. Leon Sanchez, Separably differentially closed fields, 2023. Preprint

(http://arxiv.org/abs/2302.11319).

[22] W. Johnson, C. Tran, E. Walsberg, and J. Ye, The Etale-open topology and the stable fields

conjecture, 2020. (arXiv:2101.07782). To appear in Journal of the European Mathematical

Society.

[23] Itay Kaplan, Thomas Scanlon, and Frank 0. Wagner, Artin-Schreier extensions in NIP and

simple fields, Israel Journal of Mathematics 185 (2011), no. 1, 141-153.

[24] E. R. Kolchin. Differential algebra and algebraic groups. Academic Press, 1973.

[25] E. R. Kolchin. Constrained extensions of differential fields. Advances in Mathematics, 12:141170, 1974.

[26] P. Kowalski. Derivations of the Frobenius map. Journal of Symbolic Logic, 70(1):99-110, 2005.

[27] 0. Leon Sanchez, Geometric axioms for differentially closed field in several commuting derivations. Journal of Algebra, 362:107-116, 2012. (Corrigendum, 382:332-334, 2013.)

[28] 0. Leon Sanchez, Relative D-groups and differential Galois theory in several derivations.

Transactions AMS, 367: 7613-7638, 2015.

[29] 0. Leon Sanchez, On the model companion of partial differential fields with an automorphism.

Israel Journal of Mathematics, 2016.

[30] 0. Leon Sanchez, ALGEBRO-GEOMETRIC AXIOM FOR DCFo,m- Fundamenta Mathematicae, 243, 1, p. 1-8, 2018.

[31] 0. Leon Sanchez, and M. Tress!. Differentially large fields. To appear in Algebra and Number

Theory, 2023.

[32] A. Macintyre, w1-categorical fields, Fundamenta Mathematicae 70 (1971) no. 3, 253-270.

[33] D. Marker, M. Messmer, A. Pillay. Model theory of fields. Lecture Notes in Logic 5. Springer,

1996.

[34] R. Moosa and T. Scanlon. Jet and prolongation spaces. Journal of the Inst. of Math. Jussieu

9, pp.391-430, 2010.

[35] M. Morley. Categoricity in power. Transactions of the Amer. Math. Soc., 114:514-538, 1965.

[36] J. Nagloo and A. Pillay, On Algebraic relations between solutions of a generic Painleve

equation, J. Reine Angew. Math. (Crelles Journal) 726 (2017) 1-27.

[37] D. Pierce, A. Pillay. A note on the axioms for differentially closed fields of characteristic zero.

Journal of Algebra, 204:108-115, 1998.

[38] A. Pillay. Differential Galois theory I. Illinois Journal of Mathematics. Vol. 42, N. 4, 1998.

76

EXISTENTIALLY CLOSED FIELDS WITH DIFFERENCE/DIFFERENTIAL OPERATORS

[39] A. Pillay and M. Ziegler. Jet spaces of varieties over differential and difference fields. Selecta

Mathematica. New series 9, pp.579-599, 2003.

[40] A. Robinson, On the concept of differentially closed field, Bull. Res. Counc. Isr. Sect. F 8

(1959), 113-118.

[41] M. Rosenlicht, The nonminimality of the differential closure, Pacific J. Math. 52 (1974),

529-537.

[42] A. Seidenberg. Some basic theorems in differential algebra (characteristic p, arbitrary). Transactions of the Amer. Math. Soc., 73(1):174-190, 1952.

[43] S. Shelah. Uniqueness and characterization of prime models over sets for totally transcendental first-order theories, J. Symbolic Logic 37 (1972), 107-113.

[44] S. Shelah. Differentially closed fields. Israel Journal of Mathematics, 16:314-328, 1973.

[45] K. Tent and M. Ziegler. A course in model theory. Lecture Notes in Logic. Vol.40, ASL, 2012.

[46] C. Wood. The model theory of differential fields revisited. Israel Journal of Mathematics.

25:331-352, 1976.

[47] C. Wood. Notes on the stability of separably closed fields. Journal of Symbolic Logic.

44(3):412-416, 1979.

KAI INO, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF MANCHESTER, OXFORD ROAD, MANCHESTER, UNITED KINGDOM Ml3 9PL

E-mail address: kai. ino©manchester. ac. uk

...

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