A vanishing theorem for oriented intersection multiplicities

Let A be a regular local ring containing 1/2, which is either equicharacteristic, or is smooth over a d.v.r. of mixed characteristic. We prove that the product maps on derived Grothendieck-Witt groups of A satisfy the following property: given two elements with supports which do not intersect properly, their product vanishes. This gives an analogue for "oriented intersection multiplicities" of Serre's vanishing result for intersection multiplicities. It also suggests a Vanishing Conjecture for arbitrary regular local rings containing 1/2, which is analogous to Serre's (which was proved independently by Roberts, and Gillet and Soule).


Published in:
Mathematical Research Letters, 15, 447-458
Year:
2008
Keywords:
Laboratories:




 Record created 2010-11-30, last modified 2018-03-17


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)