Module sheaf

A sheaf of modules over a small space is a generalization of the concept of a module over a ring in mathematics .

definition

Let it be a small space (so it is a topological space and a sheaf of rings over it ). A sheaf of abelian groups above is an -modules (or sheaf of -modules) if for each face the Abelian group A and the modulus of Strukturhomomorphismen and are compatible. ${\displaystyle (X,{\mathcal {O}}_{X})}$ ${\displaystyle X}$ ${\displaystyle {\mathcal {O}}_{X}}$ ${\displaystyle X}$ ${\displaystyle {\mathcal {F}}}$ ${\displaystyle X}$ ${\displaystyle {\mathcal {O}}_{X}}$ ${\displaystyle {\mathcal {O}}_{X}}$ ${\displaystyle U\subset X}$ ${\displaystyle {\mathcal {F}}(U)}$ ${\displaystyle {\mathcal {O}}_{X}(U)}$ ${\displaystyle {\mathcal {F}}}$ ${\displaystyle {\mathcal {O}}_{X}}$

literature

• Hartshorne, R. - Algebraic geometry, Springer, 1997, ISBN 3-540-90244-9