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j-multiplicity
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(Definition)
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Let $(R,\frakm)$ be a Noetherian local ring with proper ideal $I$ Define $$ j(I)=\lim_{n\to \infty} \frac{(d-1)!}{n^{d-1}} \length_R(H_\frakm^0(I^n/I^{n+1})) $$ and call it the j-multiplicity of $I$ Here $H_\frakm^0(\bullet)$ is the 0-th local cohomology functor. When $I$ is $\frakm$ primary, it is same as the
Hilbert-Samuel multiplicity $e_I(R)$
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"j-multiplicity" is owned by yshen.
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(view preamble | get metadata)
Cross-references: multiplicity, functor, cohomology, proper ideal, local ring, Noetherian
This is version 3 of j-multiplicity, born on 2008-07-21, modified 2008-07-21.
Object id is 10853, canonical name is JMultiplicity.
Accessed 474 times total.
Classification:
| AMS MSC: | 13H15 (Commutative rings and algebras :: Local rings and semilocal rings :: Multiplicity theory and related topics) |
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Pending Errata and Addenda
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