Torsion Algebraic Cycles and Complex Cobordism

  title={Torsion Algebraic Cycles and Complex Cobordism},
  author={Burt Totaro},
Atiyah and Hirzebruch gave the first counterexamples to the Hodge conjecture with integral coefficients [3]. That conjecture predicted that every integral cohomology class of Hodge type (p, p) on a smooth projective variety should be the class of an algebraic cycle, but Atiyah and Hirzebruch found additional topological properties which must be satisfied by the integral cohomology class of an algebraic cycle. Here we provide a more systematic explanation for their results by showing that the… CONTINUE READING
Highly Cited
This paper has 38 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 41 references

Algebraic cycles and values of L-functions

S. Bloch
II. Duke Math. J. 52 • 1985
View 7 Excerpts
Highly Influenced

Intersection Theory

W. Fulton
Springer-Verlag, Berlin • 1984
View 20 Excerpts
Highly Influenced

The Ω-spectrum for Brown-Peterson cohomology

W. S. Wilson
part II. Am. J. Math. 97 • 1975
View 16 Excerpts
Highly Influenced

Cycles algébriques de torsion et K-théorie algébrique

J.-L. Colliot-Thélène
Arithmetic Algebraic Geometry (Trento, 1991), LNM 1553. Springer-Verlag, Berlin • 1993
View 4 Excerpts
Highly Influenced

On the complex bordism of finite complexes

P. Conner, L. Smith
II. J. Diff. Geo. 6 • 1971
View 4 Excerpts
Highly Influenced

The mod 2 cohomology rings of extra-special 2-groups and the spinor groups

D. Quillen
Math. Ann. 194 • 1971
View 15 Excerpts
Highly Influenced

Resolution of singularities of an algebraic variety over a field of characteristic 0

H. Hironaka
I, II. Ann. Math. 79 • 1964
View 5 Excerpts
Highly Influenced

The Grothendieck ring in geometry and topology

M. Atiyah
Proceedings of the International Congress of Mathematicians, Almquist and Wiksells, Boktryckeri Aktiebolag, Uppsala • 1962
View 13 Excerpts
Highly Influenced

The torsion of the group of zero cycles modulo rational equivalence

A. Roitman
Ann. Math. 111 • 1980
View 3 Excerpts
Highly Influenced

Elements of infinite filtration in complex cobordism

P. Landweber
Math. Scand. 30 • 1972
View 4 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…