We give a formulation of the abelian case of Stark’s Main Conjecture in terms of determinants of projective modules and briefly show how this formulation leads naturally to its Equivariant Tamagawa Number Conjecture (ETNC) – type integral refinements. We discuss the Rubin-Stark integral refinement of an idempotent p1 iece of Stark’s Abelian Main Conjecture. In the process, we give a new formula...

This article is concerned with proving a refined function field analogue of the Coates-Sinnott conjecture, formulated in the number field context in 1974. Our main theorem calculates the Fitting ideal of a certain even Quillen K-group in terms of special values of L-functions. The techniques employed are directly inspired by recent work of Greither and Popescu in the equivariant Iwasawa theory ...

Antje Hahnel ([email protected]) Henri Wichmann ([email protected]) Thomas Greither ([email protected]) Matthias Kappler ([email protected]) Peter Würl ([email protected]) Matthias Kotzsch ([email protected]) Helge Taubert ([email protected]) Dirk Vordermark (dirk.vordermark@medi...

Refining results of David Burns and Cornelius Greither, respectively Annette Huber and Guido Kings, we formulate and prove an equivariant version of the main conjecture of Iwasawa theory for abelian number fields.

Let L|K be a Galois extension of fields with finite Galois group G. Greither and Pareigis [GP87] showed that there is a bijection between Hopf Galois structures on L|K and regular subgroups of Perm(G) normalized by G, and Byott [By96] translated the problem into that of finding equivalence classes of embeddings of G in the holomorph of groups N of the same cardinality as G. In [CCo06] we showed...

In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that ...

The main conjectures in Iwasawa theory predict the relationship between modules and $p$-adic $L$-functions. Using a certain proved formulation of conjecture, Greither Kurihara described explicitly (initial) Fitting ideals for cyclotomic $\mathbb{Z}_p$-extensions finite abelian extensions totally real fields. In this paper, we generalize algebraic behind their work by de...

We build upon ideas developed in [9], as well as results of Greither on a strong form of Brumer’s Conjecture ([2]–[4]), and prove Rubin’s integral version of Stark’s Conjecture for imaginary abelian extensions of Q of odd prime power conductor. INTRODUCTION In the present paper, we prove Rubin’s integral version (Conjecture B, [10], §2.1) of Stark’s general conjecture (see Conjecture 5.1 in [12...

We extend two constructions of Alan Koch, exhibiting methods to construct brace blocks, that is, families group operations on a set $G$ such any them induce skew structure $G$. these by using bilinear maps and liftings endomorphisms quotient groups with respect central subgroup. provide several examples the construction, showing there are blocks which consist distinct given cardinality. One we ...

We say a tame Galois field extension L/K with Galois group G has trivial Galois module structure if the rings of integers have the property that OL is a free OK [G]-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes l so that for each there is a tame Galois field extensio...