Representations of algebraic groups in prime characteristics
Representations of automorphisms on differentials of function fields of characteristic p.
Representations of Coxeter Groups and Hecke Algebras.
Representations of integers by binary forms and the rank of the Mordell-Weil group.
Representations of non-negative polynomials having finitely many zeros
Consider a compact subset of real -space defined by polynomial inequalities . For a polynomial non-negative on , natural sufficient conditions are given (in terms of first and second derivatives at the zeros of in ) for to have a presentation of the form , a sum of squares of polynomials. The conditions are much less restrictive than the conditions given by Scheiderer in [11, Cor. 2.6]. The proof uses Scheiderer’s main theorem in [11] as well as arguments from quadratic form theory...
Representations of non-negative polynomials via KKT ideals
This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush-Kuhn-Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K.
Representations of orbifold groups and parabolic bundles.
Representations of the fundamental group and vector bundles.
Representations of the Kauffman bracket skein algebra of the punctured torus
We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary.
Représentations -adiques potentiellement cristallines
Représentations potentiellement triangulines de dimension
Les deux résultats principaux de cette note sont d’une part que si est une représentation de de dimension qui est potentiellement trianguline, alors vérifie au moins une des propriétés suivantes (1) est trianguline déployée (2) est une somme de caractères ou une induite (3) est une représentation de de Rham tordue par un caractère, et d’autre part qu’il existe des représentations de de dimension qui ne sont pas potentiellement triangulines.
R-equivalence and rationality problem for semisimple adjoint classical algebraic groups
Réseau des périodes des courbes ... (q permier).
Réseaux de Kummer et surfaces K3.
Résidu de Grothendieck et forme de Chow.
We show an explicit relation between the Chow form and the Grothendieck residue; and we clarify the role that the residue can play in the intersection theory besides its role in the division problem.
Residual intersections.
Residual representation of algebraic-geometric codes.
Residue currents and complexity problems
Residues and duality [Book]
Residues and duality for algebraic schemes