相关论文: Infinite global fields and the generalized Brauer-…

We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic…

We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to…

Given a number field $K \neq \mathbb{Q}$, in a now classic work, Stark pinpointed the possible source of a so-called Landau-Siegel zero of the Dedekind zeta function $\zeta_K(s)$ and used this to give effective upper and lower bounds on the…

The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $\Re s > 1/2$ in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be…

For a finite abelian p-group A of rank d, we define its (logarithmic) mean exponent to be the base-p logarithm of the d-th root of its cardinality. We study the behavior of the mean exponent of p-class groups in towers of number fields. By…

We complete the first stage of constructing a theory of fields not investigated before; these fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible…

A longstanding conjecture states that global symmetries should be absent in quantum gravity. By investigating large classes of Type IIB four-dimensional $\mathcal{N}=2$ effective field theories, we enlist the potential generalized global…

The numerical invariants (global) cohomological length, (global) cohomological width, and (global) cohomological range of complexes (algebras) are introduced. Cohomological range leads to the concepts of derived bounded algebras and…

Up until now, it was recognized that a large number of 2-torsion points was a technical barrier to improve the bounds for the symmetric tensor rank of multiplication in every extension of any finite field. In this paper, we show that there…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

Generalizations of GL(n) abelian Toda and $\widetilde{GL}(n)$ abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by…

We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a…

We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation…

The Ihara limit (or -constant) $A(q)$ has been a central problem of study in the asymptotic theory of global function fields (or equivalently, algebraic curves over finite fields). It addresses global function fields with many rational…

Let $E$ be a field, $p$ a prime number and $F/E$ a finitely-generated extension of transcendency degree $t$. This paper shows that if the absolute Galois group $\mathcal{G}_{E}$ is of nonzero cohomological $p$-dimension cd$_{p}(E)$, then…

The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…

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…

It is shown that any finitely generated subring of a global field has a universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring of integers and its subsequent extensions to rings of integers in…

Schertz conjectured that every finite abelian extension of imaginary quadratic fields can be generated by the norm of the Siegel-Ramachandra invariants. We shall present a conditional proof of his conjecture by means of the characters on…

The infinitesimal symmetries of a fully decomposed non-Abelian gerbe can be generated in terms of a nilpotent BRST operator, which is here constructed. The appearing fields find a natural interpretation in terms of the universal gerbe, a…