Related papers: Towers of function fields with extremal properties
We give defining equations for function fields over finite fields with many rational places. They are obtained from composita of quadratic extensions of the rational function field.
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…
We provide a recipe to construct towers of fields producing high order elements in $\mathrm{GF}(q,2^n)$, for odd $q$, and in $\mathrm{GF}(2,2 \cdot 3^n)$, for $n \ge 1$. These towers are obtained recursively by $x_{n}^2 + x_{n} = v(x_{n -…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
We give a lower bound on multiplicative orders of some elements in defined by Conway towers of finite fields of characteristic two and also formulate a condition under that these elements are primitive
To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants…
QFTs with local topological operators feature unusual sectors called "universes," which are separated by infinite-tension domain walls. We show that such systems have relevant deformations with exactly-calculable effects. These deformations…
We prove that a group acting geometrically on a thick affine building has property (T). A more general criterion for property (T) is given for groups acting on partite complexes.
We exploit the equivalence between $t$-structures and normal torsion theories on a stable $\infty$-category to show how a few classical topics in the theory of triangulated categories, i.e., the characterization of bounded $t$-structures in…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
We characterize perfectoid towers in terms of conormal cones rather than torsion parts. This result is deduced from a refined study of the relationship between torsion with respect to a principal ideal and the associated conormal cone,…
We construct a tower of fibrations approximating the derived mapping space between two simplicially enriched operads subject to mild conditions. The n-th stage of the tower is obtained by neglecting operations with more than n inputs. The…
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
We study necessary and sufficient conditions for a valued field $\KF$ with value group $G$ and residue field $\kf$ (with char $\KF$ = char $\kf$) to admit a truncation closed embedding in the field of generalized power series $\kf((G, f))$…
Given a prime $p$, a number field $\K$ and a finite set of places $S$ of $\K$, let $\K_S$ be the maximal pro-$p$ extension of $\K$ unramified outside $S$. Using the Golod-Shafarevich criterion one can often show that $\K_S/\K$ is infinite.…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.
In this paper, we investigate properties of countable stationary towers. We derive the regularity properties of sets of reals in $L(\mathbf R)$ from some properties of countable stationary towers without explicit use of strong large…
We consider residue structures $R/G$ where $(G,+)$ is an additive subgroup of a ring $(R,+,\cdot)$, not necessarily an ideal. Special instances include Krasner's construction of quotient hyperfields, and Pumpluen's construction of…
A triangular field of rational numbers is characterized, with relations to Stirling numbers 2nd, Hyperbolic functions, and centered Binomial distribution. A Generating function is given.