A quantization procedure of fields based on geometric Langlands correspondence.
A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.
Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning...
A really elementary proof of real Lüroth's theorem.
Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K is a subfield...
A recipe for finding open subsets of vector spaces with a good quotient
A refined cojecture of Mazur-Tate type for Heegner points.
A refinement of the PRV conjecture.
A regulator map for singular varieties.
A regulator map for surfaces with an isolated singularity
A remark about isogenies of elliptic curves over quadratic fields
A remark on a conjecture of Hain and Looijenga
We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all and if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.
A remark on a non-vanishing theorem of P. Deligne and G. D. Mostow.
A Remark on a Paper of Crachiola and Makar-Limanov
A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line , then ML(X×Y) = k[X]⊗ ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled.
A remark on a theorem of Chowla-Cowles.
A remark on Abel's Theorem and the mapping of linear series.
A remark on Abhyankar's space lines
A remark on Hodge cycles on moduli spaces of rank 2 bundles over curves.
A Remark on K1 of an Algebraic Surface.
A Remark on Kawamata's Paper "On the Plurigenera of Minimal Algebraic 3-Folds with K ... 0".
A remark on moduli spaces of complete intersections.
A remark on quiver varieties and Weyl groups
In this paper we define an action of the Weyl group on the quiver varieties with generic .