Publications by Eva Bayer Fluckiger

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Let K be a global field of characteristic not 2. The embedding problem for maximal tori in a classical group G can be described in terms of algebras with involution. The aim of this paper is to give an explicit description of the obstruction group to the H ...

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat étale R-algebra are isomorphic. On the other hand, ...

Let R be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution, which are rationally isomorphic and have isomorphic semisimple coradicals, are in fact isomorp ...

Let k be a field of characteristic /=2 and let W(k) be the Witt ring of k and L a finite extension of k. If L/k is a Galois extension, then the image of rL/k is contained in W(L)Gal(L/k) where rL/k:W(k)→W(L) is the canonical ring homomorphism. Rosenberg an ...

Let \alpha be a Salem number of degree d with 4 \leqslant d \leqslant 18 . We show that if d \equiv 0, 4 \ {\rm or}\ 6 \allowbreak{\rm (mod \ 8)} , then \alpha is the dynamical degree of an automorphism of a complex (non-projective) K3 surface. We define a ...

Let k be a field of characteristic

\neq

2, and let G be a finite group. The aim of this article is to give a cohomological criterion for the isomorphism of multiples of trace forms of G-Galois algebras over k. The proof uses results concerning multiples ...

We give necessary and sufficient conditions for an integral polynomial without linear factors to be the characteristic polynomial of an isometry of some even, unimodular lattice of given signature. This gives rise to Hasse principle questions, which we ans ...

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...

Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be unimodular or defined o ...

The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor p(r), where p is an odd prime number ...

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor. ...

We prove some new cases of the Grothendieck-Serre conjecture for classical groups. This is based on a new construction of the Gersten-Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue ...

The notion of Euclidean minimum of a number field is a classical one. In this paper we generalize it to central division algebras and establish some general results in this new context. ...

The aim of this paper is to revisit the question of local–global principles for embeddings of étale algebras with involution into central simple algebras with involution over global fields of characteristic not 2. A necessary and sufficient condition is gi ...

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat etale R-algebra are isomorphic. On the other hand, ...

Eva Bayer Fluckiger

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Embedding functor for classical groups and Brauer–Manin obstruction

Orders that are étale-locally isomorphic

Rationally isomorphic hermitian forms and torsors of some non-reductive groups

Unitary descent properties

Automorphisms of $K3$ surfaces, signatures, and isometries of lattices

Multiple of trace forms and algebras with involution

Isometries of lattices and Hasse principles

Automorphisms of even unimodular lattices and equivariant Witt groups

Inhomogeneous minima of mixed signature lattices

Patching And Weak Approximation In Isometry Groups

Isometries of quadratic spaces

K3 surfaces, cyclotomic polynomials and orthogonal groups

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Upper bounds for the Euclidean minima of abelian fields of odd prime power conductor

Upper bounds for Euclidean minima of algebraic number fields

Cyclotomic Fields Are Characterized by Their Trace Lattices

On the Grothendieck-Serre conjecture for classical groups

Euclidean minima and central division algebras

Embeddings of Maximal Tori in Classical Groups, Odd Degree Descent and Hasse Principles

Orders That Are Etale-Locally Isomorphic