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The degeneracy maps are defined by.

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The homology of this simplicial module is the Hochschild homology of the functor F. The above definition of Hochschild homology of commutative algebras is the special case where F is the Loday functor.

Hochschild homology

A skeleton for the category of finite pointed sets is given by the objects. Let A be a commutative k-algebra and M be a symmetric A -bimodule [ further explanation needed ].

The Hochschild homology of a commutative algebra A with coefficients in a symmetric A -bimodule M is the homology associated to the composition. It induces an isomorphism on homotopy groups in degrees 0, 1, and 2.

On the Homology Theory of General Commutative Rings

For example,. Hesselholt showed that the Hasse-Weil zeta-function of a smooth proper variety over F p can be expressed using regularized determinants involving topological Hochschild homology. From Wikipedia, the free encyclopedia.

Vanishing of Tate homology and depth formulas over local rings

Categories : Ring theory Homological algebra. On the depth of tensor products of modules Arash Sadeghi.

Symmetry in vanishing of Tate cohomology over Gorenstein rings Arash Sadeghi. References Publications referenced by this paper.


Depth for complexes, and intersection theorems Srikanth B. Remarks on a depth formula, a grade inequality and a conjecture of Auslander Tokuji Araya , Yoichi Yoshino. Modules over unramified regular local rings Maurice Auslander.

Jorgensen , Tate co homology via pinched complexes. Differential graded homological algebra, preprint — Luchezar L. Yassemi, Depth formula via complete intersection flat dimension. Parviz Sahandi , Tirdad Sharif , Siamak.