The Hochschild homology of complete intersections
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- by Klaus Wolffhardt PDF
- Trans. Amer. Math. Soc. 171 (1972), 51-66 Request permission
Abstract:
Let $\tilde {R}$ be the algebra of all convergent (or of all strictly convergent) power series in $N$ variables over a commutative field $K$ of characteristic 0 with a valuation, e.g. $\tilde {R} = K[{X_1}, \cdots ,{X_N}]$. With each $K$-algebra $R \cong \tilde {R}/\mathfrak {a}$ we associate a bigraded $R$-algebra $E$. By the powers of $\mathfrak {a}$ a filtration of the Poincaré complex of $\tilde {R}$ is induced, and $E$ is the first term of the corresponding spectral sequence. If $\mathfrak {a}$ is generated by a prime sequence in $\tilde {R},R$ is called a complete intersection, and $E$—with an appropriate simple grading—is isomorphic to the Hochschild homology of $R$. The result is applied to hypersurfaces.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 171 (1972), 51-66
- MSC: Primary 13J05; Secondary 18H15
- DOI: https://doi.org/10.1090/S0002-9947-1972-0306192-4
- MathSciNet review: 0306192