O jedenáctém a dvanáctém Hilbertově problému
On 14-dimensional quadratic forms in , 8-dimensional forms in , and the common value property.
On a conjecture of Izhboldin on similarity of quadratic forms.
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
On indefinite binary quadratic forms and quadratic ideals.
On near-neighbor quadratic forms. (Autour des formes quadratiques quasi-voisines.)
On octahedral extensions of and quadratic -curves
We give a necessary condition for a surjective representation Gal to arise from the -torsion of a -curve. We pay a special attention to the case of quadratic -curves.
On orthogonal decomposition of homogeneous polynomials
On quadratic forms of height 3 and degree . (Sur les formes quadratiques de hauteur 3 et de degré au plus 2.)
On Rank 4 Quadratic Spaces with Given Arf and Witt Invariants.
On Real Local-Global Principles.
On the annihilating ideal for trace forms
We give several examples of classes of trace forms for which the ideal of annihilating polynomials is principal. We prove, that in general, the annihilating ideal is not a principal ideal.
On the Chow groups of quadratic Grassmannians.
On the Cohomological Characterization of Real Free Pro-2-Group.
On the diophantine equation
On the ...-invariant for quadratics forms and the linkage of cyclic algebras.
On the Maximality of the Orthogonal Groups in the Symplectic Groups in Characteristic Two.
On the nonexcellence of field extensions .
On the number of square classes of a field of finite level.
On the seperation of basic semialgebraic sets by polynomials.