Related papers: Strong linkage for function fields of surfaces

The problem of efficiently characterizing degree sequences of simple hypergraphs is a fundamental long-standing open problem in Graph Theory. Several results are known for restricted versions of this problem. This paper adds to the list of…

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 consider from a geometric point of view the conjectural fundamental lemma of Langlands and Shelstad for unitary groups over a local field of positive characteristic. We introduce projective algebraic varieties over the finite residue…

The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…

We define a variant of normal basis, called a {\em Galois scaffolding}, that allows for an easy determination of valuation, and has implications for Galois module structure. We identify fully ramified, elementary abelian extensions of local…

In 1980, Faltings proved, by deep local algebra methods, a local result regarding formal functions which has the following global geometric fact as a consequence. Theorem: Let k be an algebraically closed field (of any characteristic). Let…

This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the…

Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…

We prove that a smooth complete intersection of two quadrics of dimension at least $2$ over a number field has index dividing $2$, i.e., that it possesses a rational $0$-cycle of degree $2$.

It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…

Let A be a central simple algebra over a field F. Let k_1,\ldots, k_r be cyclic extensions of F such that k_1\otimes_F\cdots \otimes_F k_r is a field. We investigate conditions under which A is a tensor product of symbol algebras where each…

We prove that for a given flat surface with conical singularities, any pair of geometric triangulations can be connected by a chain of flips.

We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…

We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.

Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…

Let $(A,\mathfrak{m})$ be a hypersurface local ring of dimension $d \geq 1$ and let $I$ be an $\mathfrak{m}$-primary ideal. We show that there is a non-negative integer $r_I$ (depending only on $I$) such that if $M$ is any non-free maximal…

We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…

This is the seventh article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It discusses an interesting class of observables localised on surfaces that attracts steadily growing attention.…

We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…

We prove Tchebotarev type theorems for function field extensions over various base fields: number fields, finite fields, p-adic fields, PAC fields, etc. The Tchebotarev conclusion - existence of appropriate cyclic residue extensions - also…