Grothendieck topologies and applications

Journal of Linear and Topological Algebra

دوره 12، شماره 02، شهریور 2023، صفحه 141-151   

نوع مقاله: Review paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.1986465.1560

نویسندگان

K. Azi؛ H. Hamraoui؛ N. Haddar^*

TAG Laboratory, Faculty of sciences, A\"{\i}n Chock Hassan II University, B.P 5366 Maarif, Casablanca, Morocco

چکیده

Following [6], we define Grothendieck topologies on a small category and describe sheaves for these Grothendieck topologies. This generalizes, in a natural way, the theory of sheaves on a topological space

کلیدواژه‌ها

Presheaves؛ sheaves؛ Grothendieck topology؛ topos؛ Zariski topology؛ Etale topology؛ Nisnevich topology

مراجع

[1] K. Azi, H. Hamraoui, Atiyah motivic theorem for the special group SLd, Gulf J. Math. 4 (4) (2016), 54-59.

[2] A. Connes, C. Cosani, Geometry of the arithmetic site, Adv. Math. 291 (2016), 274-329.

[3] A. Connes, C. Cosani, On absolute algebraic geometry the affine case, Adv. Math. 390 (2021), 390:107909.

[4] A. Connes, C. Cosani, The arithmetic site, Comptes Rendus Mathématiques. 352 (12) (2014), 971-975.

[5] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1958.

[6] A. Grothendieck, M. Artin, J. L. Verdier, Théorie des topos et cohomologie étale des schémas, Lecture Notes in Mathematics, 1972.

[7] R. Hartshorne, Algebraic geometry, Springer-Verlag, 1977.

[8] I. Karaca, O. Ege, Digital cohomology groups of certain minimal surfaces, J. Linear. Topol. Algebra. 7 (4) (2018), 293-305.

[9] J. Milnor, Algebraic K-theory and quadratic forms, Inv. Math. 9 (4) (1970), 318-344.

[10] F. Morel, V. Veovodsky, A1-homotopy theory of schemes, Publications Mathématiques de l’IHÉS. 90 (1999), 45-143.

[11] J. Riou, Opérateurs Sur la K-théorie Algébrique et Régulateurs via la Théorie Homotopique des Schémas, Ph.D. Thesis, Paris-Saclay University, 2006.

[12] T. Vergili, I. Karaka, A note on the new basis in the mod 2 Steenrod algebra, J. Linear. Topol. Algebra. 7 (2) (2018), 101-107.