Related papers: A note on integrating group scheme actions
We prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R. As applications, we give…
Suppose X is a projective toric scheme defined over a commutative ring R equipped with an ample line bundle L. We prove that its K-theory has k+1 direct summands K(R) where k is minimal among non-negative integers such that the twisted line…
We compare among themselves two different methods for the derivation of results following from the requirement of polynomial boundedness of tree-level chiral amplitudes. It is shown that the results of the algebraic approach are valid also…
This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…
The main focus of this paper is to show that the gluing of formal schemes is also a formal scheme. The algebraic approach established here also leads us to conclude when the gluing of $k$-formal schemes is a $k$-formal scheme. In addition,…
An additive action on an algebraic variety is an effective action of the vector group with an open orbit. We describe projective surfaces with du Val singularities that admit an additive action with a finite number of orbits. In particular,…
We show that every irreducible, simply connected curve on a toric affine surface X over the field of complex numbers is an orbit closure of a multiplicative group action on X. It follows that up to the action of the automorphism group…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
We formalize in Lean the following foundational result in commutative algebra: Let $R \to S$ be a faithfully flat map of (not necessarily noetherian) commutative rings, and let $P$ be an arbitrary $R$-module. Then $P$ is projective over $R$…
We present two results about the relationship between fundamental groups of quasiprojective manifolds and linear systems on a projectivization. We prove the existence of a plane curve with non-abelian fundamental group of the complement…
We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor…
We give the basic definitions of group actions on (algebraic) stacks, and prove the existence of fixed points and quotients as (algebraic) stacks.
We study integrating (that is expanding to a Hasse-Schmidt derivation) derivations, and more generally truncated Hasse-Schmidt derivations, satisfying iterativity conditions given by formal group laws. Our results concern the cases of the…
An extended summary of the lecture course given at the V School on Geometry and Physics, Bia\l owe\.za 2016, in which an algebraic approach to differentiation and integration that is characteristic for non-commutative geometry is described.
In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.
The irreducible integrable representations with finite-dimensional weight spaces of toroidal Lie algebras on which the center acts non-trivially were classified by S.Eswara Rao. In this paper we give a compact proof of the results that lead…
We generalize to the super context, the known fact that if an affine algebraic group $G$ over a commutative ring $k$ acts freely (in an appropriate sense) on an affine scheme $X$ over $k$, then the dur sheaf $X\tilde{\tilde{/}}G$ of…
In Noor (2007)[Muhammad Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput. 187 (2007) 937-943], proposed an algorithm namely \textbf{Algorithm 2.4} and established a proof to show cubic convergence. The presented…
It is demonstrated that the so-called "unavoidable quantum anomalies" can be avoided in the farmework of a special non-linear quantization scheme. A simple example is discussed in detail.
This article concerned with the issue of solving a nonlinear equation with the help of iterative method where no any derivative evaluation is required per iteration. Therefore, this work contributes to a new class of optimal eighth-order…