# Chadmark L. Schoen

- Professor of Mathematics

**External address:**191 Physics Bldg, 120 Science Drive Box 90320, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2813

**Office Hours:**

Monday 11-12 and tuesday 11-12

or by appointment

### Research Areas and Keywords

##### Geometry: Differential & Algebraic

algebraic cycles, Chow groups, Hodge conjecture, Tate conjecture, Generalized Birch and Swinnerton-Dywer conjecture, algebraic surfaces, algebraic threefolds, varieties over finite fields, Galois representations and cohomology

I work on the geometry and arithmetic of figures defined by polynomial equations. I am especially interested in the geometry of algebraic curves, surfaces, threefolds and fourfolds over the complex numbers, over numbers fields, over finite fields, over fields of transcendence degree one over finite fields and over discrete valuation rings with perfect residue field. More specifically I study elliptic surfaces, elliptic threefolds, Calabi-Yau varieties, abelian varieties and surfaces of general type. I am interested in Chow groups of algebraic varieties and the relationship between a variety's Chow groups and its arithmetic and geometric properties.

Schoen, C. “complex varieties for which the chow group mod n is not finite.” *Journal of Algebraic Geometry*, vol. 11, no. 1, Jan. 2002, pp. 41–100. *Scopus*, doi:10.1090/S1056-3911-01-00291-0.
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Schoen, C. “On certain exterior product maps of Chow groups.” *Mathematical Research Letters*, vol. 7, no. 2–3, Jan. 2000, pp. 177–94. *Scopus*, doi:10.4310/MRL.2000.v7.n2.a4.
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Schoen, Chad. “The Chow group modulo $l$ for the triple product of a general elliptic curve.” *Asian Journal of Mathematics*, vol. 4, no. 4, International Press of Boston, 2000, pp. 987–96. *Crossref*, doi:10.4310/ajm.2000.v4.n4.a15.
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Schoen, C. “On the image of the l-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field.” *Journal of the American Mathematical Society*, vol. 12, no. 3, July 1999, pp. 795–838.

Schoen, C. “Addendum to: Hodge classes on self-products of a variety with an automorphism.” *Compositio Mathematica*, vol. 114, no. 3, Dec. 1998, pp. 329–36.

Schoen, C. “An integral analog of the Tate conjecture for one dimensional cycles on varieties over finite fields.” *Mathematische Annalen*, vol. 311, no. 3, Jan. 1998, pp. 493–500. *Scopus*, doi:10.1007/s002080050197.
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Buhler, J., et al. “Cycles, L-functions and triple products of elliptic curves.” *Journal Fur Die Reine Und Angewandte Mathematik*, vol. 492, Dec. 1997, pp. 93–133.

Schoen, C. “Varieties dominated by product varieties.” *International Journal of Mathematics*, vol. 7, no. 4, Aug. 1996, pp. 541–71. *Scopus*, doi:10.1142/S0129167X9600030X.
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Gross, Benedict H., and Chad Schoen. “The modified diagonal cycle on the triple product of a pointed curve.” *Annales De L’Institut Fourier*, vol. 45, no. 3, Cellule MathDoc/CEDRAM, 1995, pp. 649–79. *Crossref*, doi:10.5802/aif.1469.
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Schoen, C. “On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field.” *Ann. Sci. École Norm. Sup.*, vol. 28, no. 4, 1995, pp. 1–50.