On descending cohomology geometrically

Achter JD, Casalaina-Martin S, Vial C (2017)
Compositio Mathematica 153(7): 1446-1478.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an abelian variety, provided the geometric coniveau is maximal. This provides an affirmative answer to Mazur's question for all uni-ruled threefolds, for instance. Concerning cohomology in degree three, we show that the image of the Abel-Jacobi map admits a distinguished model over the rationals.
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Zeitschriftentitel
Compositio Mathematica
Band
153
Ausgabe
7
Seite(n)
1446-1478
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Achter JD, Casalaina-Martin S, Vial C. On descending cohomology geometrically. Compositio Mathematica. 2017;153(7):1446-1478.
Achter, J. D., Casalaina-Martin, S., & Vial, C. (2017). On descending cohomology geometrically. Compositio Mathematica, 153(7), 1446-1478. doi:10.1112/S0010437X17007151
Achter, J. D., Casalaina-Martin, S., and Vial, C. (2017). On descending cohomology geometrically. Compositio Mathematica 153, 1446-1478.
Achter, J.D., Casalaina-Martin, S., & Vial, C., 2017. On descending cohomology geometrically. Compositio Mathematica, 153(7), p 1446-1478.
J.D. Achter, S. Casalaina-Martin, and C. Vial, “On descending cohomology geometrically”, Compositio Mathematica, vol. 153, 2017, pp. 1446-1478.
Achter, J.D., Casalaina-Martin, S., Vial, C.: On descending cohomology geometrically. Compositio Mathematica. 153, 1446-1478 (2017).
Achter, Jeffrey D., Casalaina-Martin, Sebastian, and Vial, Charles. “On descending cohomology geometrically”. Compositio Mathematica 153.7 (2017): 1446-1478.