Research Interest: Algebraic Geometry, especially algebraic cycles

Publications:

  1. Algebraic Cycles on Certain Desingularized Nodal Hypersurfaces, Math. Ann. 270, 17-27 (1985).
  2. On the geometry of a special determinental hypersurface associated to the Mumford-Horrocks vector bundle, Crelle's Journal 364, 85-111 (1986).
  3. Complex multiplication cycles on elliptic modular threefolds, Duke Math. J., 53, 771-794 (1986).
  4. Zero cycles modulo rational equivalence on some varieties over fields of transcendence degree one, in Algebraic Geometry, Bowdoin 1985, Proc. of Symp. in pure Math., 46 part 2, 463-474 (1987).
  5. Hodge classes on self-products of a variety with an automorphism, Comp. Math. 65: 3-32 (1988).
  6. On fiber products of rational elliptic surfaces with section, Math. Z. 197, 177-199 (1988).
  7. Cyclic covers of branched along v+2 hyperplanes and the generalized Hodge conjecture for certain abelian varieties, in Arithmetic of Complex Manifolds, Erlangen 1988, Springer Lecture Notes in Math. 1399, 137-154 (1989).
  8. On certain modular representations in the cohomology of algebraic curves, J. of Algebra 135, 1-18 (1990).
  9. Bounds for rational points on twists of constant hyperelliptic curves., J. f. d. reine u. angew. Math. 411, 196-204 (1990).
  10. Produkte Abelscher Varietäten und Moduln über Ordnungen, J. f. d. reine u. angew. Math. 429, 115-123 (1992).
  11. Some examples of torsion in the Griffiths group, Math. Ann. 293, 651-679 (1992).
  12. Complex multiplication cycles and a conjecture of Bloch and Beilinson, Trans. of A.M.S. 339 87-115 (1993).
  13. On Hodge structures and non-representablity of Chow groups, Compositio Math. 88 285-316 (1993).
  14. (with M. Ross) Stable quotients of periodic minimal surfaces, Communications in Analysis and Geometry. 2 451-459 (1994)
  15. On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field, Anal. Scien. École Norm. Sup. série, t. 28, 1-50 (1995)
  16. (with B. Gross) The modified diagonal cycle on the triple product of a pointed curve, Annales de L'Institut Fourier 45, p. 649-679 (1995)
  17. Varieties dominated by product varieties, Int. J. of Math 7 p. 541-571 (1996)
  18. (with Joe Buhler and Jaap Top) Cycles, L-functions and products of elliptic curves, J. reine angew. Math. 492, p. 93-133 (1997)
  19. An integral analog of the Tate Conjecture for one dimensional cycles on varieties over finite fields, Math. Ann. 311, p. 493-500 (1998)
  20. Addendum to: Hodge classes on self-products of a variety with an automorphism, Compositio Math. 114, p. 329-336 (1998)
  21. On the image of the l-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field, J. Amer. Math. Soc. 12, p. 795-838 (1999)
  22. Cohomology computations related to the l-adic Abel-Jacobi map modulo l, in The Arithmetic and Geometry of Algebraic Cycles, p. 433-466, Kluwer Academic Press (2000) .

    Preprints:

  23. Complex varieties for which the Chow group mod n is not finite

  • Last update March 9, 2000. See http://www.math.duke.edu/faculty/schoen for more current information