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Reduced Weighted Complete Intersection and Derivations

✍ Scribed by Stefan Papadima; Laurentiu Paunescu

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
160 KB
Volume
183
Category
Article
ISSN
0021-8693

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✦ Synopsis

trivial derivations of strictly negative degree. If moreover all the weights of the variables x are even it follows that the Serre spectral sequence of any orientable i fibration F ¨E ª B, with H *F s A as graded algebras, collapses at the E -term, 2 thus verifying a conjecture of Halperin. We also discuss several examples. ᮊ 1996 Academic Press, Inc.

INTRODUCTION AND STATEMENT OF RESULTS

Let ‫ކ‬ be a field of characteristic zero and let A be a weighted zerodimensional complete intersection, i.e., a commutative ‫-ކ‬algebra of the form w x As‫ކ‬ x, . . . , x rI,

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Let R, ᒊ be a complete intersection, that is, a local ring whose ᒊ-adic completion is the quotient of a regular local ring by a regular sequence. Suppose M is a finitely generated R-module. It is known that the even and odd Betti sequences of M are eventually given by polynomials of the same degree