A construction of curves over finite fields
A descent map for curves with totally degenerate semi-stable reduction
Let be a local field of residue characteristic . Let be a curve over whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- rational torsion subgroup on the Jacobian of . We also determine divisibility of line bundles on , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of .
A formula for the supersingular polynomial
A general framework for subexponential discrete logarithm algorithms
A note on the ramification of torsion points lying on curves of genus at least two
Let be a curve of genus defined over the fraction field of a complete discrete valuation ring with algebraically closed residue field. Suppose that and that the characteristic of the residue field is not . Suppose that the Jacobian has semi-stable reduction over . Embed in using a -rational point. We show that the coordinates of the torsion points lying on lie in the unique tamely ramified quadratic extension of the field generated over by the coordinates of the -torsion...
A question of the distribution of points on a curve over a finite field.
A supersingular congruence for modular forms
Almost primality of group orders of elliptic curves defined over small finite fields.
An effective Bertini theorem and the number of rational points of a normal complete intersection over a finite field
Automorphism groups of Ree type Deligne-Lusztig curves and function fields.