Given a finite, flat morphism between embeddable noetherian schemes of pure dimension 1, we define the notion direct and inverse image for generalized divisors line bundles. In case when deal with (possibly reducible, non-reduced) projective curves over field codomain curve is smooth, introduce compactified Jacobians parametrizing torsion-free rank-1 sheaves study Norm maps Jacobians. Finally, ...

Consider a quadratic cone K in the 3-dimensional projective space PG(3,q) over finite field of order q, where q is prime power. Let E (respectively, T, S) denote set all lines that are external tangent, secant) with respect to K. We characterize minimum size blocking sets line A, A one E, S, E∪T, E∪S and T∪S.

Consider a quadratic cone K in the 3-dimensional projective space PG(3,q) over finite field of order q, where q is prime power. Let E (respectively, T, S) denote set all lines that are external tangent, secant) with respect to K. We characterize minimum size blocking sets line A, A one E, S, E∪T, E∪S and T∪S.

In this paper, we prove lower and upper bounds on the achromatic pseudoachromatic indices of n-dimensional finite projective space order q.

If a finite partial projective plane can be extended to a projective plane of order n, then it can be extended by a sequence of one line extensions. We describe necessary conditions for such an extension to exist, and restrictions which can be imposed on the intermediate sequence of extensions. This method can be used to attempt to construct a projective plane of non-prime-power order. 1. Parti...

We present a deterministic polynomial time algorithm for computing the zeta function of an arbitrary variety of fixed dimension over a finite field of small characteristic. One consequence of this result is an efficient method for computing the order of the group of rational points on the Jacobian of a smooth geometrically connected projective curve over a finite field of small characteristic. ...

Under suitable hypotheses, we prove that a form of a projective homogeneous variety G/P defined over the function field of a surface over an algebraically closed field has a rational point. The method uses an algebrogeometric analogue of simple connectedness replacing the unit interval by the projective line. As a consequence, we complete the proof of Serre’s Conjecture II in Galois cohomology ...

In this article, we propose a geometric analogue of Dirichlet’s unit theorem on arithmetic varieties [18], that is, if X is a normal projective variety over a finite field and D is a pseudo-effective Q-Cartier divisor on X, does it follow that D is Q-effective? We also give affirmative answers on an abelian variety and a projective bundle over a curve.