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Global sections of structure sheaves of Keigher rings


Author: Dmitry Trushin
Journal: Proc. Amer. Math. Soc. 140 (2012), 505-511
MSC (2000): Primary 12H05
DOI: https://doi.org/10.1090/S0002-9939-2011-10932-8
Published electronically: June 22, 2011
MathSciNet review: 2846318
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Abstract: Answering a question of J. Kovacic, we show that for any Keigher ring, its differential spectrum coincides with the differential spectrum of the ring of global sections of the structure sheaf. In particular, we obtain the answer for Ritt algebras, that is, differential rings containing the rational numbers.


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  • 1. M. F. Atiyah, I. G. Macdonald. Introduction to commutative algebra. Addison-Wesley, 1969. MR 0242802 (39:4129)
  • 2. A. Buium. Ritt schemes and torsion theory. Pacific Journal of Mathematics 98 (1982), pp. 281-293. MR 650009 (84j:13028)
  • 3. A. Buium. Differential function fields and moduli of algebraic varieties. Lecture Notes in Mathematics 1226, Springer-Verlag, Berlin-New York, 1986. MR 874111 (88e:14010)
  • 4. G. Carrà Ferro. Sullo spettro differenziale di un anello differenziale. Le Mathematiche (Catania) 33 (1978), pp. 1-17. MR 612425 (82h:13018)
  • 5. G. Carrà Ferro. The ring of global sections of the structure sheaf on the differential spectrum. Rev. Roumaine Math. Pures Appl. 30 (1985), pp. 809-814. MR 826241 (87j:13036)
  • 6. G. Carrà Ferro. Kolchin schemes. Journal Pure and Applied Mathematics 94 (1972), pp. 891-954.
  • 7. W. Keigher. Adjunctions and comonads in differential algebra, Pacific Journal of Mathematics 59 (1975), pp. 99-112. MR 0392957 (52:13770)
  • 8. W. Keigher. Prime differential ideals in differential rings. Contribution to Algebra: A collection of papers dedicated to Ellis Kolchin (Bass, Cassidy, Kovacic, eds.), Academic Press, New York, 1977, pp. 239-249. MR 0485806 (58:5610)
  • 9. W. Keigher. On the structure presheaf of a differential ring. Journal of Pure and Applied Algebra 27 (1983), pp. 163-172. MR 687748 (84g:13040)
  • 10. W. Keigher. On the quasi-affine scheme of a differential ring. Advances in Mathematics 42(2) (1981), pp. 143-153. MR 641423 (83c:12023)
  • 11. W. Keigher. Differential schemes and premodels of differential fields. Journal of Algebra 79 (1982), pp. 37-50. MR 679968 (84f:13022)
  • 12. J. J. Kovacic. Differential Schemes, Differential Algebra and Related Topics, Newark, NJ, 2000, pp. 71-94. MR 1921695 (2003i:12010)
  • 13. J. J. Kovacic. Global sections of diffspec, Journal of Pure and Applied Algebra 171 (2002), pp. 265-288. MR 1904483 (2003c:12008)

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Additional Information

Dmitry Trushin
Affiliation: Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia 119991
Email: trushindima@yandex.ru

DOI: https://doi.org/10.1090/S0002-9939-2011-10932-8
Received by editor(s): July 25, 2009
Received by editor(s) in revised form: December 5, 2010
Published electronically: June 22, 2011
Additional Notes: The author was partially supported by NSF grants CCF-0964875 and 0952591
Dedicated: This paper is dedicated to Jerald J. Kovacic
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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