Callegaro, Filippo Delucchi, Emanuele 2017-06-20 We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data. To this end, we study a morphism of spectral sequences associated to certain combinatorially defined subcomplexes of the toric Salvetti category in the complexified case, and use a technical argument in order to extend the results to full generality. As a byproduct we obtain:– a “combinatorial” version of Brieskorn's lemma in terms of Salvetti complexes of complexified arrangements,– a uniqueness result for realizations of arithmetic matroids with at least one basis of multiplicity 1 application/pdf https://folia.unifr.ch/global/documents/306107 https://folia.unifr.ch/documents/306107/files/del_ica.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2017.04.017 info:eu-repo/semantics/openAccess License undefined Advances in Mathematics. - 2017, vol. 313, p. 746–802 Toric arrangements Hyperplane arrangements Cell complexes Posets Small categories without loops Combinatorial topology Orlik–Solomon algebra Salvetti complex Arithmetic matroids info:eu-repo/classification/udc/51 The integer cohomology algebra of toric arrangements http://purl.org/coar/resource_type/c_6501