Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the `-Tate pairing in terms of the action of the Frobenius on the `-torsion of the Jacobian of a genus 2 curve. We apply similar techniques to study the non-degeneracy of the `-Tate pairing restrained to subgroups of the `-torsion which are maximal isotropic with respect to the Weil pairing. First, we ded...

Let C ⊂ Pr be a general curve of genus g embedded via a general linear series of degree d. The well-known Maximal Rank Conjecture asserts that the restriction maps H(OPr(m)) → H(OC(m)) are of maximal rank; if known, this conjecture would determine the Hilbert function of C. In this paper, we prove an analogous statement for the hyperplane sections of general curves. More specifically, if H ⊂ Pr...

where C(Fq) denotes the set of Fq-rational points of the curve C. Here we will be interested in maximal(resp. minimal) curves over Fq2 , that is, we will consider curves C attaining Hasse-Weil’s upper (resp. lower) bound: #C(Fq2) = q + 1 + 2gq (resp. q + 1− 2gq). Here we are interested to consider the hyperelliptic curve C given by the equation y = x + 1 over Fq2 . We are going to determine whe...

Fix integers d, g, r such that r ≥ 3, g > 0 and d ≥ g + r. Here we prove the existence of an integral non-special curve C in an r-dimensional projective space such that deg(C) = d, pa(C) = g, C has exactly one node and C has maximal rank (i.e. it has the expected postulation), i.e., the general non-special embedding of a general curve with a single node has maximal rank. M.S.C. 2010: 14H51, 4N05.

In this paper we solve three open problems on maximal curves with Frobenius dimension 3. In particular, we prove the existence of a maximal curve with order sequence (0, 1, 3, q).

In this paper we investigate some dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve. We compute minimum distance and weight codewords of such generalized Hamming weights codes.

BACKGROUND AND PURPOSE IDH1 mutational status probably plays an important role in the predictive response for patients with astroglioma. This study explores whether DTI metrics are able to noninvasively detect IDH1 status in astrogliomas. MATERIALS AND METHODS The DTI data of 112 patients with pathologically proven astroglioma (including 25, 12, and 10 cases with IDH1 mutation and 11, 11, and...

This study tests the hypothesis that the area postrema (AP) is necessary for endogenous ANG II to chronically maintain lumbar sympathetic nerve activity (LSNA) and heart rate (HR) in conscious sodium-deprived rats. The effect of the ANG II type 1-receptor antagonist, losartan, on LSNA and HR was determined in rats that were either AP lesioned (APX) or sham lesioned. The sham rats were divided i...