124 citations · 128 across the 5 of their papers we have counts for
6 papers
Chow groups and higher congruences for the number of rational points on proper varieties over finite fields
Najmuddin Fakhruddin
Given a proper family of varieties over a smooth base, with smooth total space and general fibre, all over a finite field k with q elements, we show that a finiteness hypothesis on…
Restriction of sections of abelian schemes
Najmuddin Fakhruddin
We prove the following result: Let B be a smooth, irreducible, quasi-projective variety over the complex numbers and assume that B has a projective compactification \bar{B} such th…
Questions on self maps of algebraic varieties
Najmuddin Fakhruddin
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
Boundedness results for periodic points on algebraic varieties
Najmuddin Fakhruddin
We prove that if f is a self-map of an algebraic variety over a field K, then under certain conditions on X, f and K the set of possible periods of K-valued periodic points of f is…
Zero cycles on generic hypersurfaces of large degree
Najmuddin Fakhruddin
We show that given a smooth projective variety X over C with dim(X) > 2, an ample line bundle O(1) on X and an integer n > 1, any n distinct points on a generic hypersurface of deg…
Indecomposable Higher Chow cycles on Jacobians
Alberto Collino, Najmuddin Fakhruddin
We construct some natural cycles with trivial regulator in the higher Chow groups of Jacobians. For hyperelliptic curves we use a criterion due to J. Lewis to prove that the cycles…