1,720,966 research outputs found
Finite quotients of Galois pro- groups and rigid fields
Full text linkFor a prime number , we show that if two certain canonical finite
quotients of a finitely generated Bloch-Kato pro- group coincide, then
has a very simple structure, i.e., is a -adic analytic pro-
group. This result has a remarkable Galois-theoretic consequence: if the two
corresponding canonical finite extensions and of a
field -- with containing a primitive -th root of unity -- coincide,
then is -rigid. The proof relies only on group-theoretic tools, and on
certain properties of Bloch-Kato pro- groups.Comment: 8 pages, to appear on the Annales math\'ematiques du Qu\'ebe
Massey products in Galois cohomology and the Elementary Type Conjecture
Full text linkLet be a prime. We prove that a positive solution to Efrat's Elementary
Type Conjecture implies a positive solution to the strengthened version of
Mina\v{c}--T\^an's Massey Vanishing Conjecture in the case of finitely
generated maximal pro- Galois groups whose pro- cyclotomic character has
torsion-free image. Consequently, the maximal pro- Galois group of a field
containing a root of 1 of order (and also \sqrt{-1} if )
satisfies the strong -Massey vanishing property for every (which is
equivalent to the cup-defining -Massey product property for every , as
defined by Mina\v{c}--T\^an) in several relevant cases.Comment: Final version, published on the Journal of Number Theory, 258 (2024),
40-6
Chasing maximal pro-p Galois groups via 1-cyclotomicity
Full text linkLet be a prime. We prove that certain amalgamated free pro- products
of Demushkin groups with pro--cyclic amalgam cannot give rise to a
1-cyclotomic oriented pro- group, and thus do not occur as maximal pro-
Galois groups of fields containing a root of 1 of order . We show that other
cohomological obstructions which are used to detect pro- groups that are not
maximal pro- Galois groups - the quadraticity of
-cohomology and the vanishing of Massey products - fail
with the above pro- groups. Finally, we prove that the Mina\v{c}-T\^an
pro- group cannot give rise to a 1-cyclotomic oriented pro- group, and we
conjecture that every 1-cyclotomic oriented pro- group satisfy the strong
-Massey vanishing property for .Comment: Thorough revision of the old version (v3), revision of the previous
version following the referee's comments (v4-v6). Conjecture 1.5 (relating
Massey products and 1-cyclotomicity) has been extended to all n>
A group-theoretical version of Hilbert's theorem 90
No full textIt is shown that for a normal subgroup N of a group G, G/N cyclic, the kernel of the map Nab→> Gad satisfies the classical Hilbert 90 property (cf. Theorem A). As a consequence, if G is finitely generated, |G: N| < ∞, and all abelian groups Hab, N ⊆ H ⊆ G, are torsion free, then Na must be a pseudo-permutation module for G/N (cf. Theorem B). From Theorem A, one also deduces a non-trivial relation between the order of the transfer kernel and co-kernel which determines the Hilbert-Suzuki multiplier (cf. Theorem C). Translated into a number-theoretical setting, one obtains a strong form of Hilbert's theorem 94 (Theorem 4.1). In case that G is finitely generated and N has prime index p in G there holds a 'generalized Schreier formula' involving the torsion-free ranks of G and N and the ratio of the order of the transfer kernel and co-kernel (cf. Theorem D)
Detecting fast solvability of equations via small powerful galois groups
No full textFix an odd prime p, and let F be a field containing a primitive pth root of unity. It is known that a p-rigid field F is characterized by the property that the Galois group GF (p) of the maximal p-extension F(p)/F is a solvable group. We give a new characterization of p-rigidity which says that a field F is p-rigid precisely when two fundamental canonical quotients of the absolute Galois groups coincide. This condition is further related to analytic p-adic groups and to some Galois modules. When F is p-rigid, we also show that it is possible to solve for the roots of any irreducible polynomials in F[X] whose splitting field over F has a p-power degree via non-nested radicals. We provide new direct proofs for hereditary p-rigidity, together with some characterizations for GF (p) - including a complete description for such a group and for the action of it on F(p) - in the case F is p-rigid
Oriented right-angled Artin pro- groups and maximal pro- Galois groups
Full text linkFor a prime number we introduce and study oriented right-angled Artin
pro- groups (oriented pro- RAAGs for short)
associated to a finite oriented graph and a continuous group
homomorphism . We show
that an oriented pro- RAAG is a Bloch-Kato
pro- group if, and only if,
is an oriented pro- group
of elementary type generalizing a recent result of I. Snopche and P. Zalesskii.
Here
denotes the canonical -orientation on . We invest
some effort in order to show that oriented right-angled Artin pro- groups
share many properties with right-angled Artin pro--groups or even
discrete RAAG's, e.g., if is a specially oriented chordal graph, then
is coherent, generalizing a result of C. Droms. Moreover,
in this case has the
Positselski-Bogomolov property generalizing a result of H. Servatius, C. Droms
and B. Servatius for discrete RAAG's. If is a specially oriented
chordal graph and in case that
, then generalizing a well known result of M.
Salvetti.Comment: The differences between the 1st version (Apr'23) and the 2nd are:
correction of a couple of minor misprints, dedication to the memory of
Avinoam Man
Groups of p-absolute Galois type that are not absolute Galois groups
Full text linkLet p be a prime. We study pro-p groups of p-absolute Galois type, as defined
by Lam-Liu-Sharifi-Wake-Wang. We prove that the pro-p completion of the
right-angled Artin group associated to a chordal simplicial graph is of
p-absolute Galois type, and moreover it satisfies a strong version of the
Massey vanishing property. Also, we prove that Demushkin groups are of
p-absolute Galois type, and that the free pro-p product -- and, under certain
conditions, the direct product -- of two pro-p groups of p-absolute Galois type
satisfying the Massey vanishing property is again a pro-p group of p-absolute
Galois type satisfying the Massey vanishing property. Consequently, there is a
plethora of pro-p groups of p-absolute Galois type satisfying the Massey
vanishing property that do not occur as absolute Galois groups.Comment: Final version, as it will appear on JPA
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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