Intersection multiplicity over a two-dimensional base

Intersection multiplicity over a two-dimensional base

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Chris Skalit , University of Illinois at Chicago
Fine Hall 322

Let X be smooth over a regular, two-dimensional base scheme Y. We show that properly-meeting cycles on X intersect with positive multiplicity (in the sense of Serre's Tor-formula). When Y is one-dimensional - say, the ring of integers of a number field - we use these techniques to investigate the extent to which intersection multiplicities can detect transversality.