Related papers: Asymptotically bad towers of function fields

We prove that maximal log Fano manifolds are generalized Bott towers. As an application, we prove that in each dimension, there is a unique maximal snc Fano variety satisfying Friedman's d-semistability condition.

The problem of constructing curves with many points over finite fields has received considerable attention in the recent years. Using the class field theory approach, we construct new examples of curves ameliorating some of the known…

We prove finiteness results on integral points on complements of large divisors in projective varieties over finitely generated fields of characteristic zero. To do so, we prove a function field analogue of arithmetic finiteness results of…

In this note, we propose the modular height of an abelian variety defined over a field of finite type over Q. Moreover, we prove its finiteness property.

The ground states of an abstract model in quantum field theory are investigated. By means of the asymptotic field theory, we give a necessary and sufficient condition for that the expectation value of the number operator of ground states is…

Throughout the paper, an analytic field means a non-archimedean complete real-valued one, and our main objective is to extend to these fields the basic theory of transcendental extensions. One easily introduces a topological analogue of the…

A lesson for the new millennium from quantum field theory: Not all field-theoretic infinities are bad. Some give rise to finite, symmetry-breaking effects, whose consequences are observed in Nature.

In this note, we show that the asymptotic dimension of any building is finite and equal to the asymptotic dimension of an apartment in that building.

Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…

Let $\mathbb{F}$ be an algebraically closed field of characteristic zero. Recently, we proved that isotypic blocks are functorially equivalent over $\mathbb{F}$. In this article we provide an example of functorially equivalent blocks which…

We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field…

In the Lubin-Tate setting we compare different categories of $(\varphi_L,\Gamma_L)$-modules over various perfect or imperfect coefficient rings. Moreover, we study their associated Herr-complexes. Finally, we show that a Lubin Tate…

In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\'an…

Let $G$ be an absolutely almost simple algebraic group over a field $K$. The genus ${\bf gen}_K(G)$ of $G$ is the set of $K$-isomorphism classes of $K$-forms $G'$ of $G$ that have the same $K$-isomorphism classes of maximal $K$-tori as $G$.…

We explore higher-dimensional conformal field theories (CFTs) in the presence of a conformal defect that itself hosts another sub-dimensional defect. We refer to this new kind of conformal defect as the composite defect. We elaborate on the…

In this paper, we establish sufficient conditions for the existence of error bounds at infinity for lower semicontinuous inequality systems. We also show that the existence of an error bound at infinity of constraint systems plays an…

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 prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.

We initiate the study of Iwasawa theory for branched $\mathbb{Z}_{p}$-towers of finite connected graphs. These towers are more general than what have been studied so far, since the morphisms of graphs involved are branched covers, a…

Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and…