Algebraic and arithmetic algebraic geometry, algebraic cycles, motives, A^1-homotopy theory of schemes, Bloch's conjecture on Albanese kernel, triangulated and monoidal categories, homotopical algebra, category theory.
Main publications:
Finite-dimensional objects in distinguished triangles. Journal of Number Theory, Vol. 119 (2006), no. 1, 99–127.
(with C. Pedrini) Finite dimensional motives and the Conjectures of Murre and Beilinson. K-Theory. Vol. 550 (2003), no. 3, 243–263.
(with C. Pedrini) The Chow motive of the Godeaux surface. Algebraic Geometry, 179–195, de Gruyter, Berlin, 2002.
The middle of the diagonal for surfaces with p_g=0 and q=1. St. Petersburg Math. J., Vol. 13 (2002), no. 3, 427–440.
(with V. Chernousov) 2-torsion of the Brauer group of an elliptic curve: generators and relations. Documenta Mathematica (2001) Extra Vol., 85–120.
(with V. Yanchevskii) Reciprocity laws for simple algebras over function fields of number curves. Communications in Algebra, 28 (2000), no. 4, 1657–1683.
