Related papers: Some nilpotence theorems for algebraic cycles

A new proof of the decomposition theorem is established using a relation with a version of the local purity theorem of Deligne and Gabber adapted to complex algebraic varieties.

We prove that the Hilbert property is satisfied by certain del Pezzo surfaces of degree one and Picard rank 1 over fields finitely generated over $\mathbb{Q}$. We generalize results of the first author on elliptic surfaces and employ…

We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the…

We describe algorithms for computing the induced nilpotent orbits in semisimple Lie algebras. We use them to obtain the induction tables for the Lie algebras of exceptional type. This also yields the classification of the rigid nilpotent…

An application of the Gordan-Hilbert finite algebraic basis theorem is suggested.

We give a novel and effective criterion for algebraicity of rational normal analytic surfaces constructed from resolving the singularity of an irreducible curve-germ on $CP^2$ and contracting the strict transform of a given line and all but…

We study solvability, nilpotency and splitting property for algebraic supergroups over an arbitrary field $K$ of characteristic $\mathrm{char}\, K \ne 2$. Our first main theorem tells us that an algebraic supergroup $\mathbb{G}$ is solvable…

Let $\g$ be simple Lie algebra. We give a conceptual proof for the fact that the nilpotent orbits of height 3 are spherical. It is shown that if the highest root of $\g$ is fundamental, then $\g$ has a specific nilpotent orbit of height 3.…

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…

Let X be a smooth irreducible projective surface. The aim of this paper is to establish a version of Clifford's theorem for coherent systems on X.

Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and…

In this paper we show that every finite-dimensional Zinbiel algebra over an arbitrary field is nilpotent, extending a previous result by other authors that they are solvable.

We provide a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory. The difficulty of the proof is delegated to a simulation result pertaining to non-deterministic type-2 machines. Thus, we…

We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.

We introduce the abstract concept of supernilpotence in loop theory, and relate it to existing concepts, namely, central nilpotence and nilpotence of the multiplication group. We prove that the class of supernilpotence is greater or equal…

In this paper, Clairaut's theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the…

In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.

The Riemann-Roch theorem is of utmost importance in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of…

The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…

The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…