15 citations · 51 across the 15 of their papers we have counts for
16 papers
On the structure of elliptic curves over finite extensions of with additive reduction
Michiel Kosters, René Pannekoek
Let be a prime and let be a finite extension of . Let be an elliptic curve with additive reduction. In this paper, we study the topological group struct…
Genus growth in -towers of function fields
Michiel Kosters, Daqing Wan
Let be a function field over a finite field of characteristic and let be a geometric extension with Galois group . Let be the corresp…
On slopes of -functions of -covers over the projective line
Michiel Kosters, Hui June Zhu
Let be a -cover of the projective line over a finite field of cardinality and charac…
On the arithmetic of Z_p-extensions
Michiel Kosters, Daqing Wan
This paper contains three parts. In the first part, we give a thorough overview of the theory of Artin-Schreier-Witt extensions: this theory allows one to understand the $\mathbf{Z…
On the last fall degree of zero-dimensional Weil descent systems
Ming-Deh A. Huang, Michiel Kosters, Yun Yang +1
In this article we will discuss a new, mostly theoretical, method for solving (zero-dimensional) polynomial systems, which lies in between Gröbner basis computations and the heuris…
Notes on summation polynomials
Michiel Kosters, Sze Ling Yeo
In these short notes, we will show the following. Let F_q be a finite field and let E/\F_q be an elliptic curve. Let S_r be the rth summation/Semaev polynomial for E. Under an assu…
Polynomial maps on vector spaces over a finite field
Michiel Kosters
Let be a finite field of cardinality and let be in . Let not all constant and consider the evaluation map $f…
Presentations for quaternionic -unit groups
Ted Chinburg, Holley Friedlander, Sean Howe +5
The purpose of this paper is to give presentations for projective -unit groups of the Hurwitz order in Hamilton's quaternions over the rational field . To our knowle…
Images of polynomial maps on large fields
Michiel Kosters
A field is called large if every irreducible -curve with a -rational smooth point has infinitely many -points. Let be a perfect large field and let . C…
The algebraic theory of valued fields
Michiel Kosters
In this exposition we discuss the theory of algebraic extensions of valued fields. Our approach is mostly through Galois theory. Most of the results are well-known, but some are ne…
A short proof of a Chebotarev density theorem for function fields
Michiel Kosters
In this article we discuss a version of the Chebotarev density for function fields over perfect fields with procyclic absolute Galois groups. Our version of this density theorem di…
Deterministically generating Picard groups of hyperelliptic curves over finite fields
Michiel Kosters
Let . In this article we will present a deterministic algorithm which does the following. The input is a hyperelliptic curve of genus over a finite field of cardin…
Algebras with only finitely many subalgebras
Michiel Kosters
Let R be a commutative ring. A not necessarily commutative R-algebra A is called futile if it has only finitely many R-subalgebras. In this article we relate the notion of futility…
The subset sum problem for finite abelian groups
Michiel Kosters
Let G be a finite abelian group. For g in G and i an integer we define N(i,g) to be the number of subsets of G of size i which sum up to g. We will give a short proof, using charac…
Anisotropy and the integral closure
Michiel Kosters
Let K be a number field and let A be an order in K. The trace map from K to Q induces a non-degenerate symmetric bilinear form <,>: B x B \to Q/Z where B is a certain finite abelia…
Anisotropic modules over artinian principal ideal rings
Michiel Kosters
Let V be a finite-dimensional vector space over a field k and let W be a 1-dimensional k-vector space. Let < , >: V x V \to W be a symmetric bilinear form. Then < , > is called ani…