C∞-rings and applications
References
- Atiyah, M. F., MacDonald, I. G. (1969). Introduction to Commutative Algebra. Boulder, CO: Westview Press.
- Berni, J. C. (2018). Some algebraic and logical apects of C∞-rings. PhD thesis (in English), Instituto de Matemática e Estatística da Universidade de São Paulo (IME-USP), São Paulo, Brazil.
- Berni, J. C., Mariano, H. L. (2018). Classifying toposes for some theories of C∞-rings. South Amer. J. Logic 4(2):313–350.
- Berni, J. C., Mariano, H. L. (2019). A universal algebraic survey of C∞-rings. Available at https://arxiv.org/pdf/1904.02728.pdf.
- Berni, J. C., Mariano, H. L. (2019). Topics on smooth commutative algebra. Available at https://arxiv.org/pdf/1904.02725.pdf, 2019.
- Berni, J. C., Mariano, H. L. (2019). Von Neumann regular C∞-rings and applications. Available at https://arxiv.org/pdf/1905.09617.pdf.
- Berni, J. C., Figueiredo, R., Mariano, H. L. (2022). On the order theory for C∞-reduced C∞-rings and applications. J. Appl. Logic 9(1):93–134.
- Borisov, D., Kremnizer, K. (2018). Beyond perturbation 1: de Rham spaces. Available at https://arxiv.org/pdf/1701.06278.pdf.
- Bunge, M., Gago, F., San Luiz, A. M. (2017). Synthetic Differential Topology. Cambridge: Cambridge University Press.
- Dubuc, E. J. (1981). C∞-Schemes. Amer. J. Math. 103(4):683–690.
- Grothendieck, A., Dieudonné, J. (1960–1967). Élements de Géométrie Algebrique. Publ. Math. Inst. Hautes Etudes Sci. (Publications Mathématiques de L’Institut des Hautes Scientifiques) 4:5–214. DOI: 10.1007/BF02684778.
- Kock, A. (1981). Synthetic Differential Geometry, London Math. Soc., Lecture Notes Series 51, 1981 (1st ed.); Cambridge: Cambridge University Press, 2006 (2nd ed.).
- Joyce, D. (2019). Algebraic Geometry over C∞-Rings, Memoirs of the American Mathematical Society, Vol. 260, Number 1256. Providence, RI: American Mathematical Society. DOI: 10.1090/memo/1256.
- MacLane, S. (1998). Categories for the Working Mathematician. New York: Springer.
- MacLane, S., Moerdijk, I. (1992). Sheaves in Geometry and Logic, A First Introduction to Topos Theory. New York: Springer.
- Marshall, M. A. (1996). Spaces of Orderings and Abstract Real Spectra, Lecture Notes in Mathematics, Vol. 1636. Berlin: Springer.
- Moerdijk, I., Reyes, G. (1986). Rings of smooth functions and their localizations I. J. Algebra 99:324–336. DOI: 10.1016/0021-8693(86)90030-X.
- Moerdijk, I., Reyes, G., Quê, N.v. (1987). Rings of smooth functions and their localizations II. In: Kueker, D. W., Lopez-Escobar, E. K. G., Smith, C. H., eds. Mathematical Logic and Theoretical Computer Science, Lecture Notes in Pure and Applied Mathematics, Vol. 106. New York: Marcel Dekker, pp. 277–300.
- Moerdijk, I., Reyes, G. (1991). Models for Smooth Infinitesimal Analysis. New York: Springer.
- Spivak, D. (2010). Derived smooth manifolds. Duke Math. J. 153(1):55–128.