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Cellular A1-homology is a new homology theory for smooth algebraic varieties over a perfect field, which is often entirely computable and is expected to give the correct motivic analogue of Poincaré duality for smooth manifolds in classical topology. I will introduce cellular A1-homology, describe the precise conjectures about cellular A1-homology of smooth projective varieties and discuss how they can be verified for smooth projective rational surfaces. The talk is based on joint work with Fabien Morel.
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Cellular A1-homology is a new homology theory for smooth algebraic varieties over a perfect field, which is often entirely computable and is expected to give the correct motivic analogue of Poincaré duality for smooth manifolds in classical topology. I will introduce cellular A1-homology, describe the precise conjectures about cellular A1-homology of smooth projective varieties and discuss how they can be verified for smooth projective rational ...
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14F42 ; 14Mxx ; 55Uxx