Showing papers by "Valery A. Lunts published in 2003"
TL;DR: In this article, the authors studied the motivic Grothendieck group of algebraic vari- eties from the point of view of stable birational geometry and obtained a counterexample to a conjecture of M. Kapranov on the rationality of motivic zeta-functions.
Abstract: We study the motivic Grothendieck group of algebraic vari- eties from the point of view of stable birational geometry. In particular, we obtain a counterexample to a conjecture of M. Kapranov on the rationality of motivic zeta-functions.
153 citations
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TL;DR: The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu as mentioned in this paper, which implies the conjecture of R. Stanley on the unimodularity of the generalized $h$-vector.
Abstract: The Hard Lefschetz theorem for intersection cohomology of nonrational polytopes was recently proved by K. Karu [Ka]. This theorem implies the conjecture of R. Stanley on the unimodularity of the generalized $h$-vector. In this paper we strengthen Karu's theorem by introducing a canonical bilinear form $(\cdot ,\cdot)_{\Phi}$ on the intersection cohomology $IH(\Phi)$ of a complete fan $\Phi$ and proving the Hodge-Riemann bilinear relations for $(\cdot ,\cdot)_{\Phi}$.
24 citations
TL;DR: In this paper, the authors describe the deformation space of quasicoherent sheaves of algebras on a quasiprojective scheme X in terms of sheaf cohomology on X and X×X.
6 citations