Geodesic
An Abel–Jacobi invariant for cobordant cycles
Documenta mathematica, Tome 21 (2016), pp. 1645-1668

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We discuss an Abel–Jacobi invariant for algebraic cobordism cycles whose image in topological cobordism vanishes. The existence of this invariant follows by abstract arguments from the construction of Hodge filtered cohomology theories in joint work of Michael J.Hopkins and the author. In this paper, we give a concrete description of the Abel–Jacobi map and Hodge filtered cohomology groups for projective smooth complex varieties.
DOI : 10.4171/dm/x10
Classification : 14C25, 14F35, 14F42, 14F43, 19E15, 32Q15, 55N22
Mots-clés : cobordism, algebraic cycles, Abel-Jacobi map, Hodge filtered cohomology, Deligne cohomology 
Gereon Quick. An Abel–Jacobi invariant for cobordant cycles. Documenta mathematica, Tome 21 (2016), pp. 1645-1668. doi: 10.4171/dm/x10
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     author = {Gereon Quick},
     title = {An {Abel{\textendash}Jacobi} invariant for cobordant cycles},
     journal = {Documenta mathematica},
     pages = {1645--1668},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/x10},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x10/}
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