Related papers: Short models of global fields

Effective field theories (EFTs) are widely considered by physicists to be explanatory and to be the appropriate frameworks for modelling various phenomena at different scales. At the same time, they are known to be approximate, restricted,…

We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…

Let G be a semisimple quasi-split group defined over a global function field. We express the relative Tamagawa number of G in terms of local data including the number of types of special vertices in one orbit of the Bruhat-Tits building…

We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted…

We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…

We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…

We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…

Neukirch developed an axiomatic and explicit approach to class field theory. This was applied to local fields and number fields but was never done for global function fields since he believed that geometric approach is more suitable.…

Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…

Usual coset construction $\SU{k}\times\SU{l}/\SU{k+l}$ of Wess--Zumino conformal field theory is presented as a coset construction of minimal models. This new coset construction can be defined rigorously and allows one to calculate easily…

We review a range of reduction methods that have been, or may be useful for connecting models of the Earth's climate system of differing complexity. We particularly focus on methods where rigorous reduction is possible. We aim to highlight…

We study the analogy between number fields and function fields in one variable over finite fields. The main result is an isomorphism between the Hilbert class fields of class number one and a family of the function fields $\mathbf{F}_q(C)$…

This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.

We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.

We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose…

We construct examples of number fields which are not isomorphic but for which their idele class groups are isomorphic. We also construct examples of projective algebraic curves which are not isomorphic but for which their Jacobian varieties…

We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

We survey results on compact Clifford-Klein forms of homogeneous spaces, with a focus on recent contributions and organized around approaches via topology, geometry and dynamics. In addition, we survey results on moduli spaces of compact…