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## The Cassels-Tate pairing on polarized abelian varieties

Let (A, e) be a principally polarized abelian variety defined over a global field k, and let ..(A) be its Shafarevich-Tate group. Let ..(A)nd denote the quotient of ..(A) by its maximal divisible… Expand

## Bertini theorems over finite fields

- B. Poonen
- Mathematics
- 29 March 2002

Let X be a smooth quasiprojective subscheme of Pn of dimension m iÝ 0 over Fq. Then there exist homogeneous polynomials f over Fq for which the intersection of X and the hypersurface f = 0 is smooth.… Expand

## Cycles of quadratic polynomials and rational points on a genus-$2$ curve

- E. V. Flynn, B. Poonen, Edward F. Schaefer
- Mathematics
- 4 August 1995

It has been conjectured that for N sufficiently large, there are no quadratic polynomials in Q[z] with rational periodic points of period N. Morton proved there were none with N=4, by showing that… Expand

## Mordell-Lang plus Bogomolov

- B. Poonen
- Mathematics
- 30 August 1998

We formulate a conjecture for semiabelian varieties A over number fields that includes both the Mordell-Lang conjecture (now proven) and the Bogomolov conjecture. We prove the "Mordellic" (finitely… Expand

## Squarefree values of multivariable polynomials

- B. Poonen
- Mathematics
- 29 March 2002

Given f in Z[x_1,...,x_n], we compute the density of x in Z^n such that f(x) is squarefree, assuming the abc conjecture. Given f,g in Z[x_1,...,x_n], we compute unconditionally the density of x in… Expand

## The classification of rational preperiodic points of quadratic polynomials over ${\Bbb Q}$: a refined conjecture

- B. Poonen
- Mathematics
- 1 May 1998

## Lattice Polygons and the Number 12

- B. Poonen, F. Rodriguez-Villegas
- MathematicsAm. Math. Mon.
- 1 March 2000

TLDR

## Large torsion subgroups of split Jacobians of curves of genus two or three

- Everett W. Howe, F. Leprévost, B. Poonen
- Mathematics
- 8 September 1998

We construct examples of families of curves of genus 2 or 3 over Q whose Jacobians split completely and have various large rational torsion subgroups. For example, the rational points on a certain… Expand

## Insufficiency of the Brauer-Manin obstruction applied to étale covers

- B. Poonen
- Mathematics
- 8 June 2008

Let k be any global field of characteristic not 2. We construct a k-variety X such that X(k) is empty, but for which the emptiness cannot be explained by the Brauer-Manin obstruction or even by the… Expand

## Explicit descent for Jacobians of cyclic coevers of the projective line.

- Edward F. Schaefer, B. Poonen
- Mathematics
- 1997

We develop a general method for bounding Mordell-Weil ranks of Jacobians of arbitrary curves of the form y p = f(x). As an example, we compute the Mordell-Weil ranks over Q and Q( p 3) for a… Expand

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