In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of O X {\displaystyle {\mathcal...

Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian...

of these algebras from the tensor product diagram of commutative algebras. A generalization of the Proj construction replaces the ring S with a sheaf...

sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology...

in algebraic geometry it is simultaneously a topological space equipped with the sheaf of rings O {\displaystyle {\mathcal {O}}} . For any ideal I of R...

properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information...

exterior power (determinant) of Ω X {\displaystyle \Omega _{X}} . A sheaf of algebras is a sheaf of module that is also a sheaf of rings. Let (X, O) be a ringed...

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions...

sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext). There...

article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras for clarification...