Grothendieck topologies and applications
الموضوعات :K. Azi 1 , H. Hamraoui 2 , N. Haddar 3
1 - TAG Laboratory, Faculty of sciences, A\"{\i}n Chock Hassan II University, B.P 5366 Maarif, Casablanca, Morocco
2 - TAG Laboratory, Faculty of sciences, A\"{\i}n Chock Hassan II University, B.P 5366 Maarif, Casablanca, Morocco
3 - TAG Laboratory, Faculty of sciences, A\"{\i}n Chock Hassan II University, B.P 5366 Maarif, Casablanca, Morocco
الکلمات المفتاحية: Presheaves, sheaves, Grothendieck topology, topos, Zariski topology, Etale topology, Nisnevich topology,
ملخص المقالة :
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
[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.
