Related papers: Class field theory for open curves over local fiel…

We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…

For a projective hypersurface $X \subset \P^n$, the images of the polar maps of degree $k$ are studied. The cohomology class defined by these maps is calculated and classical results on dual varieties are presented as applications.

Let X and Y be curves over a finite field. In this article we explore methods to determine whether there is a rational map from Y to X by considering L-functions of certain covers of X and Y and propose a specific family of covers to…

Let $A$ denote an affine algebra over an algebraically closed field $k$, with $\dim A=d\geq 3$. In the light of availability of cancellation theorems for stably free modules $P$ with $rank(P)=d-1$ (corank one), we try to implement the…

We discuss the relationship between kernels, images and cokernels of morphisms between perverse sheaves and induced maps on stalk cohomology.

We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli…

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of…

The formal group law of an elliptic curve has seen recent applications to computational algebraic geometry in the work of Couveignes to compute the order of an elliptic curve over finite fields of small characteristic. The purpose of this…

We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (degree of the dual curve). Our main observation is that the use…

By a map $p:Q\to X$ of involutive quantales is meant a homomorphism $p^*:X\to Q$. Calling a map $p$ weakly open if $p^*$ has a left adjoint $p_!$ which satisfies the Frobenius reciprocity condition (i.e., $p_!$ is a homomorphism of…

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field…

We establish several compatibility results between residue maps in \'etale and Galois cohomology that arise naturally in the analysis of smooth affine algebraic curves having good reduction over discretely valued fields. These results are…

The well-known theory of Pontryagin duality provides a strong connection between the homology and cohomology theories of a profinite group in appropriate categories. A construction for taking the `profinite direct sum' of an infinite family…

We show the existence of good hyperplane sections for schemes over discrete valuation rings with good or (quasi) semistable reduction, and the existence of good Lefschetz pencils for schemes with good reduction or ordinary quadratic…

Let $U$ be a smooth and connected curve over an algebraically closed field of positive characteristic, with smooth compactification $X$. We generalize classical Geometric Class Field theory to provide a classification of fppf $G$-torsors…

This thesis introduces the notion of "relative gerbes" for smooth maps of manifolds, and discusses their differential geometry. The equivalence classes of relative gerbes are classified by the relative integral cohomology in degree three.…

We discuss, following Mikhalkin, Brugall\'e, and many others, the counting of curves on toric surfaces with prescribed genus, Newton polygon, and intersection pattern with the toric boundary divisor, both at assigned and unassigned points.…

Using a ``3 by 3 matrix trick'' we previously showed that multiplication in a C*-algebra A, an algebraic structure, is determined by the geometry of the C*-algebra of the 3 by 3 matrices with entries from A. As an application of this…

We present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties $X$ over $p$-adic fields in terms of the N\'eron-Severi group and provide a proof under additional assumptions on an…

We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under such mappings contains a fixed ball uniformly over the class.…