### A vanishing theorem for oriented intersection multiplicities, by Jean Fasel and Vasudevan Srinivas

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 multiplicites'' 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 Soulé).

Jean Fasel <jean.fasel@math.ethz.ch>

Vasudevan Srinivas <srinivas@math.tifr.res.in>