Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

A Theorem on Smoothness-- Bass-Quillen, Chow Groups and Intersection Multiplicity of Serre

S. P. Dutta
Transactions of the American Mathematical Society
Vol. 352, No. 4 (Apr., 2000), pp. 1635-1645
Stable URL: http://www.jstor.org/stable/118079
Page Count: 11
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
A Theorem on Smoothness-- Bass-Quillen, Chow Groups and Intersection Multiplicity of Serre
Preview not available

Abstract

We describe here an inherent connection of smoothness among the Bass-Quillen conjecture, the Chow-group problem and Serre's Theorem on Intersection Multiplicity. Extension of a theorem of Lindel on smoothness plays a key role in our proof of the Serre-multiplicity theorem in the geometric (resp. unramified) case. We reduce the complete case of the theorem to the above case by using Artin's Approximation. We do not need the concept of "complete Tor". Similar proofs are sketched for Quillen's theorem on Chow groups and its extension due to Gillet and Levine.

Page Thumbnails

  • Thumbnail: Page 
1635
    1635
  • Thumbnail: Page 
1636
    1636
  • Thumbnail: Page 
1637
    1637
  • Thumbnail: Page 
1638
    1638
  • Thumbnail: Page 
1639
    1639
  • Thumbnail: Page 
1640
    1640
  • Thumbnail: Page 
1641
    1641
  • Thumbnail: Page 
1642
    1642
  • Thumbnail: Page 
1643
    1643
  • Thumbnail: Page 
1644
    1644
  • Thumbnail: Page 
1645
    1645