Some Artin–schreier Towers Are Easy
نویسنده
چکیده
Towers of function fields (resp., of algebraic curves) with positive limit provide examples of curves with large genus having many rational points over a finite field. It is in general a difficult task to calculate the genus of a wild tower. In this paper, we present a method for calculating the genus of certain Artin–Schreier towers. As an illustration of our method, we obtain a very simple and unified proof for the limits of some towers that attain the Drinfeld–Vlăduţ bound or the Zink bound. 2000 Math. Subj. Class. 11R58, 14H05, 11D59, 14G15.
منابع مشابه
Isomorphisms between Artin-Schreier towers
We give a method for efficiently computing isomorphisms between towers of Artin-Schreier extensions over a finite field. We find that isomorphisms between towers of degree pn over a fixed field Fq can be computed, composed, and inverted in time essentially linear in pn. The method relies on an approximation process.
متن کاملNewton Slopes for Artin-schreier-witt Towers
We fix a monic polynomial f(x) ∈ Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves · · · → Cm → Cm−1 → · · · → C0 = A, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tow...
متن کاملFamilies of Supersingular Artin - Schreier Curves ( Preliminary Version )
In this brief note, we prove the following two Artin-Schreier curves are supersin-gular.
متن کاملA Note on the Schmid-witt Symbol and Higher Local Fields
For a local field of characteristic p > 0, K, the combination of local class field theory and Artin-Schreier-Witt theory yield what is known as the Schmid-Witt symbol. The symbol encodes interesting data about the ramification theory of p-extensions of K and we can, for example, use it to compute the higher ramification groups of such extensions. In 1936, Schmid discovered an explicit formula f...
متن کاملperversity: a Diophantine perspective
trace function 45, 46-48, 50, 51, 56, 62, 64 adapted stratification 12, 24, 26, 37, 38, 46, 48, 63, 121, 408 additive character sums 2, 7, 8, 111-158, 161-183, 270-280, 427-428 analytic rank 8, 443, 444, 445, 447, 449, 451, 453 analytic rank, geometric see "geometric analytic rank" analytic rank, quadratic see "quadratic analytic rank" Analytic Rank Theorem 445, 450-454 approximate trace fu...
متن کامل