Related papers: The coefficient field in the nilpotence conjecture…

We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for…

We prove that the weak Hilbert property ascends along a morphism of varieties over an arbitrary field of characteristic zero, under suitable assumptions.

We use the Adams spectral sequence to compute the KO-theory of all toric manifolds and certain singular toric varieties.

Let K be an algebraically closed field. We prove that a polynomial K-derivation $D$ in two variables is locally nilpotent if and only if the subgroup of polynomial K-automorphisms which commute with D admits elements whose degree is…

We show that a strong version of the geometric Merkurjev-Panin conjecture holds for the Cox category of a projective toric variety. That is, we prove that the full strong exceptional collection of Bondal-Thomsen line bundles is invariant…

Every cohomology ring isomorphism between two non-singular complete toric varieties and quasitoric manifolds, respectively, with second Betti number $2$ is realizable by a diffeomorphism and homeomorphism, respectively.

I. Panin proved in the nineties that the algebraic K-theory of twisted projective homogeneous varieties can be expressed in terms of central simple algebras. Later, Merkurjev and Panin described the algebraic K-theory of toric varieties as…

We establish a formula for the classes of certain tori in the Grothendieck ring of varieties, in terms of its lambda-structure. More explicitly, we will see that if L* is the torus of invertible elements in the n-dimensional separable…

We show that, over a field of characteristic 0, a normal, projective variety of dimension at least 4 is uniquely determined by its underlying topological space. The proof builds on previous work of Lieblich and Olsson. Version 2: many small…

We conjecture that a $p$-algebra over a complete discrete valued field $K$ contains a totally ramified purely inseparable subfield if and only if it contains a totally ramified cyclic maximal subfield. We prove the conjecture in several…

In this paper, we will prove that any $\A^3$-form over a field $k$ of characteristic zero is trivial provided it has a locally nilpotent derivation satisfying certain properties. We will also show that the result of T. Kambayashi on the…

Let G denote a connected, quasi-split reductive group over a field F that is complete with respect to a discrete valuation and that has a perfect residue field. Under mild hypotheses, we produce a subset of the Lie algebra g(F) that picks…

This survey presents recent developments concerning the Shafarevich conjecture, non-abelian Hodge theories, hyperbolicity, and the topology of complex algebraic varieties, as well as the interplay among these areas. More precisely, we…

The biduality and reflexivity theorems are known to hold for projective varieties defined over fields of characteristic zero, and to fail in positive characteristic. In this article, we construct a notion of reflexivity and biduality in…

We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of…

In this paper we prove the Geyer-Jarden conjecture on the torsion part of the Mordell-Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian…

We totally classify the projective toric varieties whose canonical divisors are divisible by their dimensions. In Appendix, we show that Reid's toric Mori theory implies Mabuchi's characterization of the projective space for toric…

This partly expository paper investigates versions of the Tate conjecture on the cycle map for varieties defined over finite fields with values in 'etale cohomology with Z_\ell-coefficients. The bulk of the paper is an exposition of a 1998…

In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism admits a lifting to these quotient presentations. We show that…

For quasi-projective varieties over a higher local field $k_N$, we prove that its $K$-groups, above a suitable degree, are divisible-by-finite. We also prove the finiteness of the prime-to-$p$ torsion subgroup of certain higher Chow groups…