Publications associées à Function field of an algebraic variety

Some Mordell-Weil lattices and applications to sphere packings

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields. In some cases, these families of elliptic curve ...

EPFL2024

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Eva Bayer Fluckiger, Ting-Yu Lee

Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...

Hebrew Univ Magnes Press2023

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Gauthier Leterrier

We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...

SPRINGER INT PUBL AG2022

On the projectivity of some moduli spaces of varieties

Quentin Arthur Frantisek Posva

This thesis is constituted of one article and three preprints that I wrote during my PhD thesis. Their common theme is the moduli theory of algebraic varieties. In the first article I study the Chow--Mumford line bundle for families of uniformly K-stable F ...

EPFL2022

On p-adic Versions of the Manin-Mumford Conjecture

Vlad Serban

We establish p-adic versions of the Manin-Mumford conjecture, which states that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of certain rigid analytic s ...

OXFORD UNIV PRESS2021

Lower bounds for Pythagoras numbers of function fields

David Maximilian Grimm

We show that the transcendence degree of a real function field over an arbitrary real base field is a strict lower bound for its Pythagoras number and a weak lower bound for all its higher Pythagoras numbers. ...

European Mathematical Soc2015

Sums Of Squares In Algebraic Function Fields Over A Complete Discretely Valued Field

David Maximilian Grimm

A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants. ...

Pacific Journal Mathematics2014

Bounds for the Euclidean minima of function fields

Piotr Aleksander Maciak

In this paper, we define Euclidean minima for function fields and give some bound for this invariant. We furthermore show that the results are analogous to those obtained in the number field case. (C) 2013 The Authors. Published by Elsevier Inc. All rights ...

Academic Press Inc Elsevier Science2014

Splitting fields of conics and sums of squares of rational functions

David Maximilian Grimm

Given a geometrically unirational variety over an infinite base field, we show that every finite separable extension of the base field that splits the variety is the residue field of a closed point. As an application, we obtain a characterization of functi ...

Springer-Verlag2013

Algebraic Divisibility Sequences Over Function Fields

Valéry Aurélien Mahé

In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields define ...

Australian Mathematical Society2012