Related papers: Differential Weil descent
We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t)=N_{K/k}(z): firstly for quartic extensions of number fields K/k and quadratic polynomials…
In this paper we generalize the Ritt-Kolchin method of characteristic sets and the classical Gr\"obner basis technique to prove the existence and obtain methods of computation of multivariate difference-differential dimension polynomials…
We present a survey on Weil sums in which an additive character of a finite field $F$ is applied to a binomial whose individual terms (monomials) become permutations of $F$ when regarded as functions. Then we indicate how these Weil sums…
This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal…
We describe all polarizations for all abelian varieties over a finite field in a fixed isogeny class corresponding to a squarefree Weil polynomial, when one variety in the isogeny class admits a canonical liftings to characteristic zero,…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
In this note, we formulate a "one-sided" version of Wormald's differential equation method. In the standard "two-sided" method, one is given a family of random variables which evolve over time and which satisfy some conditions including a…
We first present an intersection theory of partial differential varieties with quasi-generic differential hypersurfaces. Then based on the generic intersection theory, we define the partial differential Chow form for an irreducible partial…
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
In this paper we construct a tilting sheaf for Severi-Brauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring whose semisimple component consists of…
We begin a systematic investigation of derived categories of smooth projective toric varieties defined over an arbitrary base field. We show that, in many cases, toric varieties admit full exceptional collections. Examples include all toric…
Let $\cal A$ be a maximal (or more generally a hereditary) order in a central simple algebra over a global field $F$ of positive characteristic. We study the reduction of the modular scheme of $\cal A$-elliptic sheaves at all places of $F$.…
A variation of Dyck paths allows for down-steps of arbitrary length, not just one. This is motivated by ideas published by Emeric Deutsch around the turn of the millenium. We are interested in the subclass of them where the sequence of the…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
In this paper, we use (bi)semicosimplicial language to study the classical problem of infinitesimal deformations of a closed subscheme in a fixed smooth variety, defined over an algebraically closed field of characteristic 0. In particular,…
We highlight a striking difference in behavior between two widely used variants of coordinate ascent variational inference: the sequential and parallel algorithms. While such differences were known in the numerical analysis literature in…
We introduce new natural generalizations of the classical descent and inversion statistics for permutations, called width-$k$ descents and width-$k$ inversions. These variations induce generalizations of the excedance and major statistics,…
We use Galois descent to construct central extensions of twisted forms of split simple Lie algebras over rings. These types of algebras arise naturally in the construction of Extended Affine Lie Algebras. The construction also gives…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…