𝒜 -Schemes and Zariski-Riemann Spaces
Rendiconti del Seminario Matematico della Università di Padova, Tome 127 (2012), pp. 121-178. 
@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},
     pages = {121--178},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {127},
     year = {2012},
     mrnumber = {2978003},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2012__127__121_0/}
}
TY  - JOUR
AU  - Takagi, Satoshi
TI  - $\mathcal {A}$-Schemes and Zariski-Riemann Spaces
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2012
SP  - 121
EP  - 178
VL  - 127
PB  - Seminario Matematico of the University of Padua
UR  - http://archive.numdam.org/item/RSMUP_2012__127__121_0/
LA  - en
ID  - RSMUP_2012__127__121_0
ER  - 
%0 Journal Article
%A Takagi, Satoshi
%T $\mathcal {A}$-Schemes and Zariski-Riemann Spaces
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2012
%P 121-178
%V 127
%I Seminario Matematico of the University of Padua
%U http://archive.numdam.org/item/RSMUP_2012__127__121_0/
%G en
%F RSMUP_2012__127__121_0
Takagi, Satoshi. $\mathcal {A}$-Schemes and Zariski-Riemann Spaces. Rendiconti del Seminario Matematico della Università di Padova, Tome 127 (2012), pp. 121-178. http://archive.numdam.org/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 | Zbl

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

[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 | Zbl

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

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

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

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

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

[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