Algebraic Cobordism Ii
نویسنده
چکیده
We complete and extend the construction of algebraic cobordism from [4]. Let k be a field admitting resolution of singularities, let Schk denote the category of finite type schemes over a field k, and let Smk be the full subcategory of smooth quasiprojective k-schemes. For an l.c.i. morphism f : X → Y of finite type k-schemes, we define a functorial pullback morphism f ∗. With these pull-back maps, Ω∗ becomes what we call a oriented Borel-Moore homology theory on Schk. Restricting Ω∗ to smooth quasi-projective k-schemes, this defines Ω∗ as an oriented cohomology theory on Smk. Relying on the results of [4], we show that Ω∗ is the universal oriented Borel-Moore homology theory on Schk and the universal oriented cohomology theory on Smk. This completes the proofs of some of the main results of [4]. In addition, we extend the results of [4] concerning Rost’s degree formulas from smooth k-schemes to local-complete-intersection k-schemes (for k of characteristic zero).
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