Related papers: Bertini theorems admitting base changes
A well-known theorem of Wedderburn asserts that a finite division ring is commutative. In a division ring the group of invertible elements is as large as possible. Here we will be particularly interested in the case where this group is as…
Stability plays a central role in arithmetic. In this article, we explain some basic ideas and present certain constructions for such studies. There are two aspects: namely, general Class Field Theories for Riemann surfaces using…
There are classical theorems of analysis which, given certain conditions on a perturbation, assert stability of the essential and absolutely continuous components of the spectrum of a self-adjoint operator. Whereas the singular component is…
Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…
Replacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable enlargement of the class of rings with stable rank one (B-rings), and…
We give the new effective criterion for the global generation of the adjoint bundle on normal surfaces with a boundary. We could make the invariant \delta small a bit more on log-terminal singular point, and then we could prove the theorem…
We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…
We study just infinite algebras which remain so upon extension of scalars by arbitrary field extensions. Such rings are called stably just infinite. We show that just infinite rings over algebraically closed fields are stably just infinite…
We show that the theories of some (ordered) central simple algebras with involution over real closed fields are model-complete or admit quantifier elimination, and characterize positive cones in terms of morphisms into models of some of…
In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\mathbb{Z}$ is interpretable by positive existential formulas in…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Let X be a smooth quasiprojective subscheme of P^n of dimension m >= 0 over F_q. Then there exist homogeneous polynomials f over F_q for which the intersection of X and the hypersurface f=0 is smooth. In fact, the set of such f has a…
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…
Stable surfaces and their log analogues are the type of varieties naturally occuring as boundary points in moduli spaces. We extend classical results of Kodaira and Bombieri to this more general setting: if $(X,\Delta)$ is a stable log…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
We deal with consistency results for the existence of universal models in natural classes of models (more exactly--a somewhat weaker version). We apply a result on quite general family to T_feq and to the class of triangle-free graphs.
We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
We study the relationship between Bell states, finite groups and complete sets of bases. We show how to obtain a set of N+1 bases in which Bell states are invariant. They generalize the X, Y and Z qubit bases and are associated to groups of…
We show the existence of good hyperplane sections for schemes over discrete valuation rings with good or (quasi) semistable reduction, and the existence of good Lefschetz pencils for schemes with good reduction or ordinary quadratic…