Related papers: Un th\'eor\`eme de Bloch presque complexe

We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of…

We give a few properties equivalent to the Bloch-Kato conjecture (now the norm residue isomorphism theorem).

We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.

A complex Lie supergroup can be described as a real Lie supergroup with integrable almost complex structure. The necessary and sufficient conditions on an almost complex structure on a real Lie supergroup for defining a complex Lie…

This paper proves a generalization of the Butterfly Theorem, a classical Euclidean result, which is valid in the complex projective plane.

We present an application of the basic mathematical concept of complex functions as topological solitons, a most interesting area of research in physics. Such application of complex theory is virtually unknown outside the community of…

The paper studies semi-almost periodic holomorphic functions on a polydisk which have, in a sense, the weakest possible discontinuities on the boundary torus. The basic result used in the proofs is an extension of the classical Bohr…

This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the…

We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a…

We introduce the notion of \emph{almost commutative Q-algebras} and demonstrate how the derived bracket formalism of Kosmann-Schwarzbach generalises to this setting. In particular, we construct `almost commutative Lie algebroids' following…

We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.

Using toric geometry we prove a B\'ezout type theorem for weighted projective spaces.

We prove a complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to the case of planks that are not necessarily centrally…

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

We investigate Bloch electrons in two dimensions subject to constant electric and magnetic fields. The model that results from our pursuit is governed by a finite difference equation with a quasienergy spectrum that interpolates between a…

We prove a uniformization theorem in complex algebraic geometry.

We prove a second main theorem for elliptic projective planes.