Tim Dokchitser
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View article: Arithmetic of hyperelliptic curves over local fields
Arithmetic of hyperelliptic curves over local fields Open
We study hyperelliptic curves $$y^2 = f(x)$$ over local fields of odd residue characteristic. We introduce the notion of a “cluster picture” associated to the curve, that describes the p -adic distances between the roots of f ( x ), and s…
View article: Character formula for Weil representations in terms of Frobenius traces
Character formula for Weil representations in terms of Frobenius traces Open
It is known that the etale cohomology of a potentially good abelian variety over a local field K is determined by its Euler factors over the extensions of K. We extend this to all abelian varieties, show that it is enough to take extension…
View article: Character formula for conjugacy classes in a coset
Character formula for conjugacy classes in a coset Open
Let $G$ be a finite group and $N
View article: Semistable types of hyperelliptic curves
Semistable types of hyperelliptic curves Open
In this paper, we explore three combinatorial descriptions of semistable types of hyperelliptic curves over local fields: dual graphs, their quotient trees by the hyperelliptic involution, and configurations of the roots of the defining eq…
View article: Arithmetic of hyperelliptic curves over local fields
Arithmetic of hyperelliptic curves over local fields Open
We study hyperelliptic curves y^2=f(x) over local fields of odd residue characteristic. We introduce the notion of a "cluster picture" associated to the curve, that describes the p-adic distances between the roots of f(x), and show that th…
View article: 3-torsion and conductor of genus 2 curves
3-torsion and conductor of genus 2 curves Open
We give an algorithm to compute the conductor for curves of genus 2. It is based on the analysis of 3-torsion of the Jacobian for genus 2 curves over 2-adic fields.
View article: Models of curves over DVRs
Models of curves over DVRs Open
Let C be a smooth projective curve over a discretely valued field K, defined by an affine equation f(x,y)=0. We construct a model of C over the ring of integers of K using a toroidal embedding associated to the Newton polygon of f. We show…
View article: GMJ volume 60 issue 1 Cover and Back matter
GMJ volume 60 issue 1 Cover and Back matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: GMJ volume 59 issue 2 Cover and Back matter
GMJ volume 59 issue 2 Cover and Back matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: Arithmetic of hyperelliptic curves over local fields
Arithmetic of hyperelliptic curves over local fields Open
We study hyperelliptic curves y^2=f(x) over local fields of odd residue characteristic. We introduce the notion of a cluster picture associated to the curve, that describes the p-adic distances between the roots of f(x), and show that this…