Related papers: Tame Galois module structure revisited

A finite group G is admissible over a field M if there is a division algebra whose center is M with a maximal subfield G-Galois over M. We consider nine possible notions of being admissible over M with respect to a subfield K of M, where…

Let S/R be a finite extension of discrete valuation rings of characteristic p>0, and suppose that the corresponding extension L/K of fields of fractions is separable and is H-Galois for some K-Hopf algebra H. Let D_{S/R} be the different of…

Let $L/K$ be a finite, totally ramified $p$-extension of complete local fields with residue fields of characteristic $p > 0$, and let $A$ be a $K$-algebra acting on $L$. We define the concept of an $A$-scaffold on $L$, thereby extending and…

For a prime \(p\ge 2\) and a number field K with p-class group of type (p,p) it is shown that the class, coclass, and further invariants of the metabelian Galois group \(G=Gal(F_p^2(K) | K)\) of the second Hilbert p-class field \(F_p^2(K)\)…

We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…

Let $A$ be a finite dimensional representation-finite algebra over an algebraically closed field. The aim of this work is to generalize the results proven in CGS. Precisely, we determine which vertices of $Q_A$ are sufficient to be…

A finite \'etale map between irreducible, normal varieties is called tame, if it is tamely ramified with respect to all partial compactifications whose boundary is the support of a strict normal crossings divisor. We prove that if the…

Let A be an abelian variety over a number field k. We show that weak approximation holds in the Weil-Ch\^atelet group of A/k but that it may fail when one restricts to the n-torsion subgroup. This failure is however relatively mild; we show…

Let $K$ be a totally real field. In this article we present an asymptotic formula for the number of Hilbert modular cusp forms $f$ with given ramification at every place $v$ of $K$. When $v$ is an infinite place, this means specifying the…

Let C/K be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of C over a field F where it becomes semistable. This allows us to describe the Galois action on the l-adic Tate module of…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…

Let p be an odd prime. The lattice of all normal subgroups and the terms of the lower and upper central series are determined for all metabelian p-groups with generator rank d=2 having abelianization of type (p,p) and minimal defect of…

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_\infty and k/Q are finite. We give a full description of the algebraic structure of the semisimple algebra QG=Quot(\Lambda G)…

Let L be an abelian number field of degree n with Galois group G. In this paper we study how to compute efficiently a normal integral basis for L, if there is at least one, assuming that the group G and an integral basis for L are known.

Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division…

We prove an effective form of Hilbert's irreducibility theorem for polynomials over a global field $K$. More precisely, we give effective bounds for the number of specializations $t\in \mathcal{O}_K$ that do not preserve the irreducibility…

Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s in N, we determine K_mE/p^sK_mE as a (Z/p^sZ)[Gal(E/F)]-module. We also provide examples of extensions for which all of the possible nonzero…

This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from…

A Galois scaffold, in a Galois extension of local fields with perfect residue fields, is an adaptation of the normal basis to the valuation of the extension field, and thus can be applied to answer questions of Galois module structure. Here…

We show that if $B$ is a block of a finite group algebra $kG$ over an algebraically closed field $k$ of prime characteristic $p$ such that $\HH^1(B)$ is a simple Lie algebra and such that $B$ has a unique isomorphism class of simple…