Related papers: On enumerating extensions of p-adic fields with gi…
We consider p-extensions of number fields such that the filtration of the Galois group by higher ramification groups is of prescribed finite length. We extend well-known properties of tame extensions to this more general setting; for…
We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the…
We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method…
We develop the topological polylogarithm which provides an integral version of Nori's Eisenstein cohomology classes for $GL_n(\mathbf{Z})$ and yields classes with values in an Iwasawa algebra. This implies directly the integrality…
In this paper we present an iterative construction of irreducible polynomials over finite fields based upon repeated applications of transforms induced by endomorphisms of odd prime degree of ordinary elliptic curves.
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…
We enumerate the number of isoclinism classes of semi-extraspecial $p$-groups with derived subgroup of order $p^2$. To do this, we enumerate $\text{GL}(2, p)$-orbits of sets of irreducible, monic polynomials in $\mathbb{F}_p[x]$. Along the…
We prove a simultaneous generalization of the classical Riemann-Hurwitz and Plucker formulas, addressing the total inflection of a morphism from a (smooth, projective) curve to an arbitrary (smooth, projective) higher-dimensional variety.…
Let $F$ be a local field over $\mathbf{Q}_p$ or $\mathbf{F}_p((t))$, and let $D$ be a central simple division algebra over $F$ of degree $d$. In the $p$-adic case, we assume $p>de+1$ where $e$ is the ramification degree over $\mathbf{Q}_p$;…
We study the higher ramification structure of dynamical branch extensions, and propose a connection between the natural dynamical filtration and the filtration arising from the higher ramification groups: each member of the former should,…
Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.
We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We deduce a classification of any Galois cubic extension of a…
We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…
A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz's formula extends, essentially without change, to a count of…
For a given length and a given degree and an arbitrary partition of the positive integers, there always is a cell containing a polynomial progression of that length and that degree; moreover, the coefficients of the generating polynomial…
We study in detail the valuation theory of deeply ramified fields and introduce and investigate several other related classes of valued fields. Further, a classification of defect extensions of prime degree of valued fields that was earlier…
We give an efficient algorithm to enumerate all sets of $r\ge 1$ quadratic polynomials over a finite field, which remain irreducible under iterations and compositions.
In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…
We construct a dual exponential map which relates the $p$-adic Eisenstein classes to Eisenstein series. From this map, we deduce a compatibility between the $p$-adic realization and the de Rham realization of the torsion sections of the…
In this paper, a construction of complete permutation polynomials over finite fields of even characteristic proposed by Tu et al. recently is generalized in a recursive manner. Besides, several classes of complete permutation polynomials…