Related papers: Galois theory and projective geometry

Calculational abstract interpretation, long advocated by Cousot, is a technique for deriving correct-by-construction abstract interpreters from the formal semantics of programming languages. This paper addresses the problem of deriving…

We prove the conjecture that two projective symplectic resolutions for a symplectic variety $W$ are related by Mukai's elementary transformations over $W$ in codimension 2 in the following cases: (i). nilpotent orbit closures in a classical…

This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…

In this paper we connect classical differential geometry with the concepts from geometric calculus. Moreover, we introduce and analyze a more general Laplacian for multivector-valued functions on manifolds. This allows us to formulate a…

We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.

In the present paper, we study the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields from the point of view of anabelian geometry. In particular, we show that, under certain mild assumptions, the…

We generalize the notion of a projective profinite group to a projective pair of a profinite group and a closed subgroup. We establish the connection with Pseudo Algebraically Closed (PAC) extensions of PAC fields: Let M be an algebraic…

This is an essay to accompany the author's lecture at the introductory workshop on `Nonabelian fundamental groups in arithmetic geometry' at the Newton Institute, Cambridge in July, 2009.

This is a survey for the 2015 AMS Summer Institute on Algebraic Geometry about the Frobenius type techniques recently used extensively in positive characteristic algebraic geometry. We first explain the basic ideas through simple versions…

This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…

We take some initial steps towards illuminating the (hypothetical) $p$-adic local Langlands functoriality principle relating Galois representations of a $p$-adic field $L$ and admissible unitary Banach space representations of $G(L)$ when…

We define vector fields, leaves and trajectories for schemes. With these tools, we are able to give a geometrical interpretation and to generalize several results of differential Galois theory and constructions on differential schemes. We…

In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…

This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.

In this paper we discuss algebraic, combinatorial and topological properties of singular virtual braids. On the algebraic side we state the relations between classical and virtual singular objects, in addition we discuss a Birman-like…

After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such…

We prove that any projective Schur algebra over a field $K$ is equivalent in $Br(K)$ to a radical abelian algebra. This was conjectured in 1995 by Sonn and the first author of this paper. As a consequence we obtain a characterization of the…

The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain…

This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomorphisms on these abelian varieties and the images of the…

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this…