Chadmark L. Schoen
- Professor of Mathematics
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.
Ross, Marty, and Chad Schoen. “Stable quotients of periodic minimal surfaces.” Communications in Analysis and Geometry, vol. 2, no. 3, International Press of Boston, 1994, pp. 451–59. Crossref, doi:10.4310/cag.1994.v2.n3.a4. Full Text
Schoen, C. “Complex multiplication cycles and a conjecture of beilinson and bloch.” Transactions of the American Mathematical Society, vol. 339, no. 1, Jan. 1993, pp. 87–115. Scopus, doi:10.1090/S0002-9947-1993-1107030-6. Full Text
Schoen, C. “On Hodge structures and nonrepresentability of Chow groups.” Compositio Math., vol. 88, 1993, pp. 285–316.
Schoen, C. “Produkte Abelscher Varietäten und Moduln Über Ordnungen.” Journal Fur Die Reine Und Angewandte Mathematik, vol. 1992, no. 429, Jan. 1992, pp. 115–24. Scopus, doi:10.1515/crll.1992.429.115. Full Text
Schoen, C. “On certain modular representations in the cohomology of algebraic curves.” Journal of Algebra, vol. 135, no. 1, Nov. 1990, pp. 1–18. Scopus, doi:10.1016/0021-8693(90)90147-G. Full Text
Schoen, C. “Bounds for rational points on twists of constant hyperelliptic curves.” Journal Fur Die Reine Und Angewandte Mathematik, vol. 1990, no. 411, Jan. 1990, pp. 196–204. Scopus, doi:10.1515/crll.1990.411.196. Full Text
Schoen, C. “On fiber products of rational elliptic surfaces with section.” Mathematische Zeitschrift, vol. 197, no. 2, June 1988, pp. 177–99. Scopus, doi:10.1007/BF01215188. Full Text
Schoen, C. “Hodge classes on self-products of a variety with an automorphism.” Compositio Mathematica, vol. 65, Foundation Compositio Mathematica, 1988, pp. 3–32.
Schoen, C. “Complex multiplication cycles on elliptic modular threefolds.” Duke Mathematical Journal, vol. 53, no. 3, Sept. 1986, pp. 771–94. Manual, doi:10.1215/S0012-7094-86-05343-3. Full Text