Results 1 to 10 of about 600 (183)
Cohomological Dimension and Schreier's Formula in Galois Cohomology [PDF]
Canadian Mathematical Bulletin, 2007 AbstractLet p be a prime and F a field containing a primitive p-th root of unity. Then for n ∈ N, the cohomological dimension of the maximal pro-p-quotient G of the absolute Galois group of F is at most n if and only if the corestriction maps are surjective for all open subgroups H of index p. Using this result, we generalize Schreier's formula for .
John Labute +3 more
openalex +4 more sources
On the monoidal invariance of the cohomological dimension of Hopf algebras [PDF]
Comptes Rendus. Mathématique, 2022 We discuss the question of whether the global dimension is a monoidal invariant for Hopf algebras, in the sense that if two Hopf algebras have equivalent monoidal categories of comodules, then their global dimensions should be equal.
Bichon, Julien
doaj +2 more sources
Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension [PDF]
Forum of Mathematics, Pi, 2022 We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions and derive applications regarding the local cohomological dimension, the Du Bois complex, local ...
Mircea Mustaţă, Mihnea Popa
doaj +2 more sources
Cohomological dimension and arithmetical rank of some determinantal ideals [PDF]
Le Matematiche, 2015 Let M be a (2 × n) non-generic matrix of linear forms in a polynomial ring. For large classes of such matrices, we compute the cohomological dimension (cd) and the arithmetical rank (ara) of the ideal I_2(M) generated by the 2-minors of M.
Davide Bolognini +3 more
doaj +2 more sources
Cohomological dimension of complexes [PDF]
Communications in Algebra, 2003 In the derived category of the category of modules over a commutative Noetherian ring $R$, we define, for an ideal $\fa$ of $R$, two different types of cohomological dimensions of a complex $X$ in a certain subcategory of the derived category, namely $\cd(\fa, X)=\sup\{\cd(\fa, \H_{\ell}(X))-\ell|\ell\in\Bbb Z\}$ and $-\inf{\mathbf R}\G_{\fa}(X ...
Mohammad T. Dibaei, Siamak Yassemi
openalex +4 more sources
Topological calculation of local cohomological dimension [PDF]
Journal of Singularities, 2021 We show that the sum of the local cohomological dimension and the rectified $\mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological dimension is then calculated using the cohomology of the links of the analytic space.
Thomas Reichelt +2 more
openalex +3 more sources
Strong Cohomological Dimension [PDF]
Bulletin of the Polish Academy of Sciences Mathematics, 2008 We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps.
Jerzy Dydak, Akira Koyama
openalex +2 more sources
Groebner deformations, connectedness and cohomological dimension [PDF]
Journal of Algebra, 2008 17 ...
Matteo Varbaro
openalex +5 more sources
On The Cohomological Dimension of Local Cohomology Modules [PDF]
, 2015 Let $R$ be a Noetherian ring, $I$ an ideal of $R$ and $M$ an $R$-module with $\operatorname{cd}(I,M)=c$. In this article, we first show that there exists a descending chain of ideals $I=I_c\supsetneq I_{c-1}\supsetneq \cdots \supsetneq I_0$ of $R$ such that for each $0\leq i\leq c-1$, $\operatorname{cd}(I_i,M)=i$ and that the top local cohomology ...
V. Erdoǧdu, Tuğba Yıldırım
openalex +2 more sources
The role of cohomology in quantum computation with magic states [PDF]
Quantum, 2023 A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this web to quantum computation with magic states.
Robert Raussendorf +3 more
doaj +1 more source