Related papers: Everywhere ramified towers of global function fiel…
We consider a tower of function fields F=(F_n)_{n\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \mathcal{E):=(EF_n)_{n\goq 0} is a tower over the field F_q. Then we deal with the following: What can we…
This paper gives examples of function fields $K_0$ over a finite field $\mathbb{F}_q$ of $p$ power order ramified only at one finite regular prime over $\mathbb{F}_q(t)$, which admit infinite Hilbert $p$-class field towers. Such a $K_0$ can…
Certain towers of function fields with complete splitting of rational places at each stage are constructed. Also, families oof towers with positive N/g ratios are described.
This paper studies infinite class field towers of number fields $K$ that are ramified over $\Q$ only at one finite prime. In particular, we show the existence of such towers for a general family of primes including $p=2$, 3 and 5.
In this work, we use the notion of ``symmetry'' of functions for an extension $K/L$ of finite fields to produce extensions of a function field $F/K$ in which almost all places of degree one split completely. Then we introduce the notion of…
In this paper we construct Galois towers with good asymptotic properties over any non-prime finite field $\mathbb F_{\ell}$; i.e., we construct sequences of function fields $\mathcal{N}=(N_1 \subset N_2 \subset \cdots)$ over $\mathbb…
The explicit construction of function fields tower with many rational points relative to the genus in the tower play a key role for the construction of asymptotically good algebraic-geometric codes. In 1997 Garcia, Stichtenoth and Thomas…
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara's quantity $A(\ell)$, for $\ell = p^n$ with $p$…
In this paper we study general conditions to prove the infiniteness of the genus of certain towers of function fields over a perfect field. We show that many known examples of towers with infinite genus are particular cases of these…
We give effective bounds for the class number of any algebraic function field of genus $g$ defined over a finite field. These bounds depend on the possibly partial information on the number of places on each degree $\leq g$. Such bounds are…
We give a construction and equations for good recursive towers over any finite field $\mathbf{F}_q$ with $q \ne 2$ and $3$.
In this paper we study the problem of constructing non-trivial subtowers and supertowers of recursive towers of function fields over finite fields.
In this work, we give sufficient conditions in order to have finite ramification locus in sequences of function fields defined by different kind of Kummer extensions. These conditions can be easily implemented in a computer to generate…
In a previous work general conditions were given to prove the infiniteness of the genus of certain towers of function fields over a perfect field. It was shown that many examples where particular cases of those general results. In this…
For every prime number p, we show the existence of a solvable number field L ramified only at {p and infinity whose p-Hilbert Class field tower is infinite.
Let us consider an algebraic function field defined over a finite Galois extension $K$ of a perfect field $k$. We give some conditions allowing the descent of the definition field of the algebraic function field from $K$ to $k$. We apply…
In this work we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bound for the parameters of the obtained codes. In a particular case of a tower over $\mathbb{F}_{q^2}$ for any odd $q$,…
Up until now, it was recognized that a large number of 2-torsion points was a technical barrier to improve the bounds for the symmetric tensor rank of multiplication in every extension of any finite field. In this paper, we show that there…
Recently Bassa, Garcia and Stichtenoth constructed a tower of function fields over GF(q^3) having many rational places relative to their genera. We show that, by removing the bottom field from this tower, we obtain the same tower we would…
The form factor bootstrap in integrable quantum field theory allows one to capture local fields in terms of infinite sequences of Laurent polynomials called `towers'. For the sine-Gordon model, towers are systematically described by…