Torsion on non-integral schemes and singular sheaves of dimension one
Alain Leytem
Broschiertes Buch

Torsion on non-integral schemes and singular sheaves of dimension one

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In Part I we analyze the torsion of a module over a non-integral ring and the torsion of a sheaf on a non-integral scheme. We give an explicit definition of the torsion subsheaf of a quasi-coherent sheaf and prove a condition under which it is also quasi-coherent. Using the associated primes of a module and the primary decomposition of ideals, we review the main criteria for torsion-freeness and purity of a sheaf. We also discuss properties of the restriction of a coherent sheaf to its annihilator and its Fitting support and prove that sheaves of pure dimension are torsion-free on their suppor...