19 citations · 28 across the 7 of their papers we have counts for
6 papers · 1 filter
Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant
Eric Rains, Karl Rubin, Travis Scholl +2
We show that if a rational map is constant on each isomorphism class of unpolarized abelian varieties of a given dimension, then it is a constant map. Our results are motivated by…
Geometry of Biquadratic and Cyclic Cubic Log-Unit Lattices
Fernando Azpeitia Tellez, Christopher Powell, Shahed Sharif
By Dirichlet's Unit Theorem, under the log embedding the units in the ring of integers of a number field form a lattice, called the log-unit lattice. We investigate the geometry of…
Period and index for higher genus curves
Shahed Sharif
Given a curve over a field , the period of is the gcd of degrees of -rational divisor classes, while the index is the gcd of degrees of -rational divisors. S. Li…
Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
Lisa Berger, Chris Hall, René Pannekoek +5
We study the Jacobian of the smooth projective curve of genus with affine model over the function field , when is p…
Period, index and potential sha
Pete L. Clark, Shahed Sharif
In this paper we advance the theory of O'Neil's period-index obstruction map and derive consequences for the arithmetic of genus one curves over global fields. Our first result imp…
Period and index of genus one curves over number fields
Shahed Sharif
The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of…