Contributions to the study of Cartier algebras and local cohomology modules

  1. Boix, Alberto F.
Supervised by:
  1. Josep Àlvarez Montaner Director
  2. Santiago Zarzuela Director

Defence university: Universitat de Barcelona

Fecha de defensa: 20 November 2014

  1. Joan Elías García Chair
  2. Dolors Herbera Espinal Secretary
  3. Luis Narváez Macarro Committee member

Type: Thesis

Teseo: 384894 DIALNET lock_openTDX editor


This dissertation is devoted to the study of Cartier algebras and local cohomology modules; more precisely, we show that the Cartier algebra of a complete Stanley-Reisner ring R can only be either principally generated or infinitely generated as R-algebra, and that such issue just depends on the primary decomposition of the corresponding Stanley-Reisner ideal. Secondly, we provide an algorithm in order to calculate all the ideals which are fixed with respect to the action of any principally generated Cartier subalgebra of the Cartier algebra associated to the polynomial ring Z/pZ[x(1),…, x(d)], where p is a prime number. Finally, we produce spectral sequences which recover and extend the Mayer-Vietoris spectral sequence of local cohomology modules established in full generality by G. Lyubeznik; moreover, we find conditions in order to ensure when these spectral sequences degenerate at their second page and, in such case, we study their attached extension problems.