Related papers: Witt equivalence of function fields of curves over…

The framework of universal geometry allows us to consider metrical properties of affine views of elliptic curves, even over finite fields. We show how the Neuberg cubic of triangle geometry extends to the finite field situation and provides…

We extend the theory of spinor class field and representation fields previously defined for lattices over the ring of integers of a number field to both, lattices over the coordinate ring of a smooth irreducible affine curve over a finite…

The difference between slice and doubly-slice knots is reflected in algebra by the difference between metabolic and hyperbolic Blanchfield linking forms. We exploit this algebraic distinction to refine the classical Witt group of linking…

We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories.…

We show that the points of a global function field, whose classes are 2-divisible in the Picard group, form a connected graph, with the incidence relation generalizing the well known quadratic reciprocity law. We prove that for every global…

We expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of…

We prove the vanishing modulo torsion of the higher direct images of the sheaf of Witt vectors (and the Witt canonical sheaf) for a purely inseparable projective alteration between normal finite quotients over a perfect field. For this, we…

We associate to any endomorphism of the punctured affine space over some field an element in the Witt group of the base field that we call degree. We use this degree to give a counter-example to a question on unimodular rows

Suppose that $F$ is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve with positive self-intersection. We prove that if there exists a non-constant meromorphic function on $F$, then the…

This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum field theory over 2-dimensional quantum gravity up to algebraic…

Consider the collection of edge bicolorings of a graph that is cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and…

We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greater than or equal to the characteristic of the field, which is…

In algebraic geometry there is a well-known categorical equivalence between the category of normal proper integral curves over a field $k$ and the category of finitely generated field extensions of $k$ of transcendence degree $1$. In this…

This paper present the construction cyclic isodual codes over finite fields and finite chain rings. These codes are monomially equivalent to their dual. Conditions are given for the existence of cyclic isodual codes. In addition, the…

We prove that there exists, up to isomorphism, exactly one function field over the finite field of two elements of class number one and genus four. This result, together with the ones of MacRae, Madan, Leitzel, Queen and Stirpe, establishes…

The periods of arbitrary abelian forms on hyperelliptic Riemann surfaces, in particular the periods of the meromorphic Seiberg-Witten differential, are shown to be in one-to-one correspondence with the conformal blocks of correlation…

It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…

Let $\mathcal{G}$ be a smooth linear group scheme of finite type. For any positive integer $k$ and a finite field $\mathbb{F}$, let $W_k(\mathbb{F})$ be the ring of Witt vectors of length $k$ over $\mathbb{F}$. We show that the group…

We associate strand diagrams to tilings of surfaces with marked points, generalising Scott's method for triangulations of polygons. We thus obtain a map from tilings of surfaces to permutations of the marked points on boundary components,…

A possible connection between quantum computing and Zeta functions of finite field equations is described. Inspired by the 'spectral approach' to the Riemann conjecture, the assumption is that the zeroes of such Zeta functions correspond to…