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Betti Numbers of Modules of Exponent Two over Regular Local Rings

✍ Scribed by Shou-Te Chang

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
271 KB
Volume
193
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let R, m, K be a regular local ring of dimension n and let M be a finite length module over R. This paper gives an affirmative answer to Horrocks' questions when m 2 M s 0, that is, in this case the rank of the ith syzygy of M is at

and the ith Betti number of M is at least .

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## Abstract Let __K__ be the quotient field of a 2‐dimensional regular local ring (__R, m__) and let __v__ be a prime divisor of __R__, i.e., a valuation of __K__ birationally dominating __R__ which is residually transcendental over __R__. Zariski showed that: such prime divisor __v__ is uniquely a