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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Hochschild homology of complete intersections


Author: Klaus Wolffhardt
Journal: Trans. Amer. Math. Soc. 171 (1972), 51-66
MSC: Primary 13J05; Secondary 18H15
MathSciNet review: 0306192
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0306192-4
PII: S 0002-9947(1972)0306192-4
Keywords: Hochschild homology, analytic algebra, affinoid algebra, affine algebra, formal differentials, complete intersection, hypersurface
Article copyright: © Copyright 1972 American Mathematical Society