Related papers: Ahlfors theorems for differential forms

We prove modularity lifting theorems for l-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type condition at l. This extends the results of Clozel, Harris and Taylor, and the…

This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…

The recent theory of fractional $h$-difference equations introduced in [N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional variational problems, Signal Process. 91 (2011), no. 3, 513--524], is enriched with useful…

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

In this paper, we generalize Ahlfors' lemma on logarithmic derivative to holomorphic tangent curves of directed projective manifolds intersecting closed subschemes. As a consequence, we obtain Algebro-Geometric Ahlfors' Lemma on Logarithmic…

We prove an analog of Lagrange's Theorem for continued fractions on the Heisenberg group: points with an eventually periodic continued fraction expansion are those that satisfy a particular type of quadratic form, and vice-versa.

It is shown that quantized irreducible flag manifolds possess a canonical $q$-analogue of the de Rham complex. Generalizing the well known situation for the standard Podle\'s' quantum sphere this analogue is obtained as the universal…

Examples of Fell algebras with compact spectrum and trivial Dixmier-Douady invariant are constructed to illustrate differences with the case of continuous trace $C^*$-algebras. At the level of the spectrum, this translates to only assuming…

There is proposed the Maillet--Malgrange type theorem for a generalized power series (having complex power exponents) formally satisfying an algebraic ordinary differential equation. The theorem describes the growth of the series…

We give some new congruences for singular real algebraic curves which generalize Fiedler's congruence for nonsingular curves.

New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…

A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…

We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.

A generalization of classical theorems on the existence of sections of real, complex and quaternionic Stiefel manifolds is proved.

We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential equations. Using related techniques, we also give a…

We establish several analogues of the classical Lidskii Theorem for some special classes of singular traces (Dixmier traces and Connes-Dixmier traces) used in noncommutative geometry.

We revisit Ahlfors theory of covering surfaces thanks to Stokes theorem.

An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.

We construct open-closed maps on various versions of Hochschild and cyclic homology of the Fukaya $A_\infty$ algebra of a Lagrangian submanifold modeled on differential forms. The $A_\infty$ algebra may be curved. Properties analogous to…

Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…