Geodesic
Aspects of Enumerative Geometry with Quadratic Forms
Documenta mathematica, Tome 25 (2020), pp. 2179-2239
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Using the motivic stable homotopy category over a field k, a smooth variety X over k has an Euler characteristic χ(X/k) in the Grothendieck-Witt ring GW(k). The rank of χ(X/k) is the classical Z-valued Euler characteristic, defined using singular cohomology or étale cohomology, and the signature of χ(X/k) under a real embedding σ:k→R gives the topological Euler characteristic of the real points Xσ(R).
DOI : 10.4171/dm/797
Classification : 14C17, 14F42
Mots-clés : Chow-Witt groups, Euler characteristics, Euler classes, Grothendieck-Witt ring 
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     author = {Marc Levine},
     title = {Aspects of {Enumerative} {Geometry} with {Quadratic} {Forms}},
     journal = {Documenta mathematica},
     pages = {2179--2239},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/797},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/797/}
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Marc Levine. Aspects of Enumerative Geometry with Quadratic Forms. Documenta mathematica, Tome 25 (2020), pp. 2179-2239. doi: 10.4171/dm/797

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