Related papers: Taylor conditions over finite fields

We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y $\subset$ X a subvariety, then X satisfies generically the scheme-theoretic Whitney condition a along Y…

In this paper we obtain a Poitou-Tate exact sequence for finite and flat group schemes over a global function field. We also extend the duality theorems for 1-motives over number fields obtained by D.Harari and T.Szamuely to the function…

We obtain Liouville type theorems for degenerate elliptic equation with a drift term and a potential. The diffusion is driven by H\"ormander operators. We show that the conditions imposed on the coefficients of the operator are optimal.…

We prove several new Bertini theorems over arbitrary fields and discrete valuation rings.

One extends P. Deligne's notion of integrality over a finite field for a $\ell$-adic sheaf on a scheme of finite type over a local field with finite residue field. One shows that this integrality notion is preserved by $Rf_!$, as it is over…

We develop relativistic causality theory in the setting of point-free topology by introducing a notion of causal coverage in ordered locales, generalising their canonical coverage relation to incorporate causal structure. This improves…

We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear setting (i.e. arithmetic progressions), the nonlinear nature of…

We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…

According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters provided that the right sides of the differential…

In this article, we prove a generalisation of the Mertens theorem for prime numbers to number fields and algebraic varieties over finite fields, paying attention to the genus of the field (or the Betti numbers of the variety), in order to…

The paper has two purposes. First, we start to develop a theory of infinite global fields, i.e., of infinite algebraic extensions either of ${\mathbb{Q}}$ or of ${\mathbb{F}}_r(t)$. We produce a series of invariants of such fields, and we…

We provide an introductory exposition to the sheaf topos theoretic description of classical field theory motivated by the rigorous description of both $\bf{(i)}$ the variational calculus of (infinite dimensional) field-theoretic spaces, and…

We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii theorems for systems of algebraic differential conditions over differentially closed fields. Namely, given a system of algebraic conditions on the first $l$ derivatives…

Permutation polynomials over finite fields have taken an important role in vast areas in mathematics as well as engineering. Recently, Tu et al. gave some classes of complete permutation polynomials over finite fields of even…

We prove a Frobenius-type theorem for singular distributions generated by a family of locally Lipschitz continuous vector fields satisfying almost everywhere a quantitative finite type condition.

We consider non-linear changes of variables and Fubini's theorem for certain integrals over a two-dimensional local field. An interesting example is presented in which imperfectness of a finite characteristic local field causes Fubini's…

According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters providing the right sides of the differential…

We prove Bertini type theorems and give some applications of them. The applications are in the context of Lefschetz theorem for Nori fundamental group for normal varieties as well as for geometric formal orbifolds. In another application,…

This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.

We prove finiteness results on integral points on complements of large divisors in projective varieties over finitely generated fields of characteristic zero. To do so, we prove a function field analogue of arithmetic finiteness results of…