𝒜 -Schemes and Zariski-Riemann Spaces
Takagi, Satoshi
Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012), p. 121-178 / Harvested from Numdam
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Publié le : 2012-01-01
@article{RSMUP_2012__127__121_0,
     author = {Takagi, Satoshi},
     title = {$\mathcal {A}$-Schemes and Zariski-Riemann Spaces},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {128},
     year = {2012},
     pages = {121-178},
     mrnumber = {2978003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2012__127__121_0}
}

Takagi, Satoshi. $\mathcal {A}$-Schemes and Zariski-Riemann Spaces. Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012) pp. 121-178. http://gdmltest.u-ga.fr/item/RSMUP_2012__127__121_0/

[CN] W. W. Comfort - S. Negrepontis, The theory of ultrafilters, Grundlehren der mathematischen Wissenschaften 211 (1974), Springer-Verlag. | MR 396267 | Zbl 0298.02004

[Con] B. Conrad, Deligne's notes on Nagata compactifications, J. Ramanujan Math. Soc., 22, no. 3 (2007), pp. 205-257. | MR 2356346 | Zbl 1142.14001

[EGA4] A. Grothendieck, Éléments de Géométrie Algébrique IV. Étude locale des schémas et des morphisms de schémas, Inst. Hautes Études Sci. Publ. Math., no. 32 (1967). | Numdam | MR 238860 | Zbl 0153.22301

[KS] M. Kashiwara - P. Schapira, Categories and sheaves, Grundlehren der mathematischen Wissenschaften 332 (2006), Springer-Verlag. | MR 2182076 | Zbl 1118.18001

[CWM] S. Maclane, Categories for the working mathematician, Graduate Texts in Mathematics, vol. 5 (1998), 2nd edition, Springer-Verlag. | MR 1712872 | Zbl 0906.18001

[Mat] H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Math. no. 8 (1986), Cambridge University Press. | MR 879273 | Zbl 0603.13001

[Nag] M. Nagata, Imbedding of an abstract variety in a complete variety, J. Math. Kyoto, 2, no. 1 (1962), pp. 1-10. | MR 142549 | Zbl 0109.39503

[Ste] V. Steven, Locales and toposes as spaces, Handbook of Spatial Logics, Springer (2007), Chap. 8. | MR 2393892

[Tak] S. Takagi, Construction of schemes over 𝔽 1 , and over idempotent rings: towards tropical geometry, preprint (arXiv:1009.0121).

[Tem] M. Temkin, Relative Riemann-Zariski space, preprint (arXiv:0804.2843v1), to appear in Israel Journal of Mathematics. | MR 2837126 | Zbl pre06108370