相关论文: Towers of function fields with extremal properties

This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental…

We prove that every perfectoid tower can be decomposed into a fiber product of perfectoid towers that are either $p$-torsion free or perfect of characteristic $p$. As an application, we show that separated perfectoid towers are reduced. We…

In this article we investigate some "unexpected" properties of the "Infinite Power Tower". \[y = f(x) = {x^{{x^{{x^{{x^ {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} }}}}}}}\] The…

We answer a question of Peikert and Rosen by giving for each $\epsilon > 0$ an efficient construction of infinite families of number fields $N$ such that the root discriminant $D_N^{1/[N:\mathbb{Q}]}$ is bounded above by a constant times…

We derive the effective potential for composite fields in a class of (quasi-) planar models with long-range interactions. This class of models can be relevant for high temperature superconductors and graphite. The fractal structure of the…

Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…

Some boundedness properties of function spaces (considered as topological groups) are studied.

A twin building consists of two buildings that are twinned by a codistance function. We prove that the local structure of a twin building uniquely determines the two buildings up to isomorphism. This has been known for twin buildings…

In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture…

A completely reducible subcomplex of a spherical building is a spherical building.

The number A(q) is the upper limit of the ratio of the maximum number of points of a curve defined over $\Fq$ to the genus. By constructing class field towers with good parameters we present improvements of lower bounds of A(q) for q an odd…

This paper studies infinite class field towers of number fields $K$ that are ramified over $\Q$ only at one finite prime. In particular, we show the existence of such towers for a general family of primes including $p=2$, 3 and 5.

We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these…

We introduce two new types of towers of Drinfeld modular curves. These towers originate from a specific domain $\mathcal{A} $ and are analogous to the towers of rank-two Drinfeld modular curves over the polynomial ring. Specifically, the…

We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields…

We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…

We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable…

We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…

We define left relative H-separable tower of rings and continue a study of these begun by Sugano. It is proven that a progenerator extension has right depth two if and only if the ring extension together with its right endomorphism ring is…

In this paper, we investigate the unit groups, the $2$-class groups, the $2$-class field towers and the structures of the second $2$-class groups of some multiquadratic number fields of degree $8$ and $16$.