The Serre Problem for Discrete Hodge Algebras.
The set of points at which a polynomial map is not proper
We describe the set of points over which a dominant polynomial map is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by .
The sixtieth anniversary of the Jacobian Conjecture: a new approach
We investigate an approach of Bass to study the Jacobian Conjecture via the degree of the inverse of a polynomial automorphism over an arbitrary ℚ-algebra.
The Strong Anick Conjecture is true
Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra over a field of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...
The Structure of Certain Ideal Transforms.
The Waring loci of ternary quartics.
Toward an arithmetic of polynomials.
Transfer of the notion of -rings to fibre products. (Transfert de la notion de -anneaux aux produits fibres.)
Truncations of the ring of number-theoretic functions.
Two Examples of the Bass-Quillen-Suslin Conjectures.