309 research outputs found
NMR analysis reveals extensive binding interactions of complex xyloglucan oligosaccharides with the Cellvibrio japonicus Glycoside Hydrolase Family 31 -xylosidase
No full textThe study of the interaction of glycoside hydrolases with their substrates is fundamental to diverse applications in medicine, food and feed production, and biomass-resource utilization. Recent molecular modeling of the a-xylosidase CjXyl31A from the soil saprophyte Cellvibrio japonicus, together with protein crystallography and enzyme-kinetic analysis, has suggested that an appended PA14 protein domain, unique among glycoside hydrolase family 31 members, may confer specificity for large oligosaccharide fragments of the ubiquitous plant polysaccharide xyloglucan (J. Larsbrink, A. Izumi, F. M. Ibatullin, A. Nakhai, H. J. Gilbert, G. J. Davies, H. Brumer, Biochem. J. 2011, 436, 567580). In the present study, a combination of NMR spectroscopic techniques, including saturation transfer difference (STD) and transfer NOE (TR-NOE) spectroscopy, was used to reveal extensive interactions between CjXyl31A active-site variants and xyloglucan hexa- and heptasaccharides. The data specifically indicate that the enzyme recognizes the entire cello-tetraosyl backbone of the substrate and product in positive enzyme subsites and makes further significant interactions with internal pendant a-(1?6)-linked xylosyl units. As such, the present analysis provides an important rationalization of previous kinetic data on CjXyl31A and unique insight into the role of the PA14 domain, which was not otherwise obtainable by protein crystallography.</p
A non-abelian brumer-Stark conjecture
No full textLa recherche d’annulateurs du groupe des classes d’idéaux d’une extension abélienne de Q est un sujet classique et remonte à des travaux de Kummer et Stickelberger. La conjecture de Brumer-Stark porte sur les extensions abéliennes de corps de nombres et prédit qu’un élément de l’anneau de groupe du groupe de Galois, appelé élément de Brumer-Stickelberger, est un annulateur du groupe des classes de l’extension. De plus, elle stipule que les générateurs des idéaux principaux obtenus possèdent des propriétés bien particulières. Cette thèse est dédiée à la généralisation de cette conjecture aux extensions de corps de nombres galoisiennes mais non abéliennes. Dans un premier temps, nous nous focalisons sur l’étude de l’analogue non abélien de l’élément de Brumer, nécessaire à l’établissement d’une conjecture non abélienne. La seconde partie est consacrée à l’énoncé de la conjecture de Brumer-Stark non abélienne et à ses reformulations, ainsi qu’aux propriétés qu’elle vérifie. Nous nous intéressons notamment aux propriétés de changement d’extension. Nous étudions ensuite le cas spécifique des extensions dont le groupe de Galois possède un sous-groupe abélien H distingué d’indice premier. Sous la validité de la conjecture de Brumer-Stark associée à certaines extensions abéliennes, nous en déduisons deux résultats suivant la parité du cardinal de H : dans le cas impair, nous démontrons la conjecture de Brumer-Stark non abélienne, et dans le cas pair, nous établissons un résultat d’abélianité permettant d’obtenir, sous des hypothèses supplémentaires, la conjecture non abélienne. Enfin nous effectuons des vérifications numériques de la conjecture non abélienne permettant de démontrer cette conjecture dans les exemples testés.Finding annihilators of the ideal class group of an abelian extension of Q is a classical subject which goes back to work of Kummer and Stickelberger. The Brumer-Stark conjecture deals with abelian extensions of number fields and predicts that a group ring element, called the Brumer-Stickelberger element, annihilates the ideal class group of the extension under consideration. Moreover it specifies that the generators thus obtained have special properties. The aim of this work is to generalize this conjecture to non-abelian Galois extensions. We first focus on the study of a non-abelian analogue of the Brumer element, necessary to establish a non-abelian generalization of the conjecture. The second part is devoted to the statement of our non-abelian conjecture, and the properties it satisfies. We are particularly interested in extension change properties. We then study the specific case of extensions whose Galois group has an abelian normal subgroup H of prime index. If the Brumer-Stark conjecture associated to certain abelian subextensions holds, we prove two results according to the parity of the cardinal of H : in the odd case, we get the non-abelian Brumer-Stark conjecture, and in the even case, we establish an abelianity result implying under additional hypotheses the proof of the non-abelian conjecture. Thanks to PARI-GP, we finally do some numerical verifications of the nonabelian conjecture, proving its validity in the tested examples
On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture
No full textThis is the final version. Available from Springer via the DOI in this record.We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases.The first named author acknowledges financial support
provided by EPSRC First Grant EP/N005716/1 ‘Equivariant Conjectures in Arithmetic’.
The second named author acknowledges financial support provided by the DFG within
the Collaborative Research Center 701 ‘Spectral Structures and Topological Methods in
Mathematics’
Conjecture de brumer-stark non abélienne
No full textFinding annihilators of the ideal class group of an abelian extension of Q is a classical subject which goes back to work of Kummer and Stickelberger. The Brumer-Stark conjecture deals with abelian extensions of number fields and predicts that a group ring element, called the Brumer-Stickelberger element, annihilates the ideal class group of the extension under consideration. Moreover it specifies that the generators thus obtained have special properties. The aim of this work is to generalize this conjecture to non-abelian Galois extensions. We first focus on the study of a non-abelian analogue of the Brumer element, necessary to establish a non-abelian generalization of the conjecture. The second part is devoted to the statement of our non-abelian conjecture, and the properties it satisfies. We are particularly interested in extension change properties. We then study the specific case of extensions whose Galois group has an abelian normal subgroup H of prime index. If the Brumer-Stark conjecture associated to certain abelian subextensions holds, we prove two results according to the parity of the cardinal of H : in the odd case, we get the non-abelian Brumer-Stark conjecture, and in the even case, we establish an abelianity result implying under additional hypotheses the proof of the non-abelian conjecture. Thanks to PARI-GP, we finally do some numerical verifications of the nonabelian conjecture, proving its validity in the tested examples.La recherche d’annulateurs du groupe des classes d’idéaux d’une extension abélienne de Q est un sujet classique et remonte à des travaux de Kummer et Stickelberger. La conjecture de Brumer-Stark porte sur les extensions abéliennes de corps de nombres et prédit qu’un élément de l’anneau de groupe du groupe de Galois, appelé élément de Brumer-Stickelberger, est un annulateur du groupe des classes de l’extension. De plus, elle stipule que les générateurs des idéaux principaux obtenus possèdent des propriétés bien particulières. Cette thèse est dédiée à la généralisation de cette conjecture aux extensions de corps de nombres galoisiennes mais non abéliennes. Dans un premier temps, nous nous focalisons sur l’étude de l’analogue non abélien de l’élément de Brumer, nécessaire à l’établissement d’une conjecture non abélienne. La seconde partie est consacrée à l’énoncé de la conjecture de Brumer-Stark non abélienne et à ses reformulations, ainsi qu’aux propriétés qu’elle vérifie. Nous nous intéressons notamment aux propriétés de changement d’extension. Nous étudions ensuite le cas spécifique des extensions dont le groupe de Galois possède un sous-groupe abélien H distingué d’indice premier. Sous la validité de la conjecture de Brumer-Stark associée à certaines extensions abéliennes, nous en déduisons deux résultats suivant la parité du cardinal de H : dans le cas impair, nous démontrons la conjecture de Brumer-Stark non abélienne, et dans le cas pair, nous établissons un résultat d’abélianité permettant d’obtenir, sous des hypothèses supplémentaires, la conjecture non abélienne. Enfin nous effectuons des vérifications numériques de la conjecture non abélienne permettant de démontrer cette conjecture dans les exemples testés
Conjecture de brumer-stark non abélienne
No full textFinding annihilators of the ideal class group of an abelian extension of Q is a classical subject which goes back to work of Kummer and Stickelberger. The Brumer-Stark conjecture deals with abelian extensions of number fields and predicts that a group ring element, called the Brumer-Stickelberger element, annihilates the ideal class group of the extension under consideration. Moreover it specifies that the generators thus obtained have special properties. The aim of this work is to generalize this conjecture to non-abelian Galois extensions. We first focus on the study of a non-abelian analogue of the Brumer element, necessary to establish a non-abelian generalization of the conjecture. The second part is devoted to the statement of our non-abelian conjecture, and the properties it satisfies. We are particularly interested in extension change properties. We then study the specific case of extensions whose Galois group has an abelian normal subgroup H of prime index. If the Brumer-Stark conjecture associated to certain abelian subextensions holds, we prove two results according to the parity of the cardinal of H : in the odd case, we get the non-abelian Brumer-Stark conjecture, and in the even case, we establish an abelianity result implying under additional hypotheses the proof of the non-abelian conjecture. Thanks to PARI-GP, we finally do some numerical verifications of the nonabelian conjecture, proving its validity in the tested examples.La recherche d’annulateurs du groupe des classes d’idéaux d’une extension abélienne de Q est un sujet classique et remonte à des travaux de Kummer et Stickelberger. La conjecture de Brumer-Stark porte sur les extensions abéliennes de corps de nombres et prédit qu’un élément de l’anneau de groupe du groupe de Galois, appelé élément de Brumer-Stickelberger, est un annulateur du groupe des classes de l’extension. De plus, elle stipule que les générateurs des idéaux principaux obtenus possèdent des propriétés bien particulières. Cette thèse est dédiée à la généralisation de cette conjecture aux extensions de corps de nombres galoisiennes mais non abéliennes. Dans un premier temps, nous nous focalisons sur l’étude de l’analogue non abélien de l’élément de Brumer, nécessaire à l’établissement d’une conjecture non abélienne. La seconde partie est consacrée à l’énoncé de la conjecture de Brumer-Stark non abélienne et à ses reformulations, ainsi qu’aux propriétés qu’elle vérifie. Nous nous intéressons notamment aux propriétés de changement d’extension. Nous étudions ensuite le cas spécifique des extensions dont le groupe de Galois possède un sous-groupe abélien H distingué d’indice premier. Sous la validité de la conjecture de Brumer-Stark associée à certaines extensions abéliennes, nous en déduisons deux résultats suivant la parité du cardinal de H : dans le cas impair, nous démontrons la conjecture de Brumer-Stark non abélienne, et dans le cas pair, nous établissons un résultat d’abélianité permettant d’obtenir, sous des hypothèses supplémentaires, la conjecture non abélienne. Enfin nous effectuons des vérifications numériques de la conjecture non abélienne permettant de démontrer cette conjecture dans les exemples testés
On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture
No full textWe show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases
On the Brumer-Stark Conjecture
No full textLet be a finite abelian extension of number fields with totally
real and a CM field. Let and be disjoint finite sets of places of
satisfying the standard conditions. The Brumer-Stark conjecture states that
the Stickelberger element annihilates the -smoothed
class group . We prove this conjecture away from , that
is, after tensoring with . We prove a stronger version of this
result conjectured by Kurihara that gives a formula for the 0th Fitting ideal
of the minus part of the Pontryagin dual of in terms of Stickelberger elements.
We also show that this stronger result implies Rubin's higher rank version of
the Brumer-Stark conjecture, again away from 2.
Our technique is a generalization of Ribet's method, building upon on our
earlier work on the Gross-Stark conjecture. Here we work with group ring valued
Hilbert modular forms as introduced by Wiles. A key aspect of our approach is
the construction of congruences between cusp forms and Eisenstein series that
are stronger than usually expected, arising as shadows of the trivial zeroes of
-adic -functions. These stronger congruences are essential to proving
that the cohomology classes we construct are unramified at .Comment: 99 pages (A reference is updated in the new version
On the equality of three formulas for Brumer-Stark units
No full textDasgupta S, Honnor MHL, Spieß M. On the equality of three formulas for Brumer-Stark units. Journal of the London Mathematical Society . 2025;112(4): e70296.We prove the equality of three conjectural formulas for Brumer-Stark units. The first formula has essentially been proven, so this paper also verifies the validity of the other two formulas
Brumer-Stark Units and Explicit Class Field Theory
No full textLet be a totally real field of degree and an odd prime. We prove
the -part of the integral Gross--Stark conjecture for the Brumer--Stark
-units living in CM abelian extensions of . In previous work, the first
author showed that such a result implies an exact -adic analytic formula for
these Brumer--Stark units up to a bounded root of unity error, including a
``real multiplication'' analogue of Shimura's celebrated reciprocity law from
the theory of Complex Multiplication. In this paper we show that the
Brumer--Stark units, along with other easily described elements (these
are simply square roots of certain elements of ) generate the maximal
abelian extension of . We therefore obtain an unconditional construction of
the maximal abelian extension of any totally real field, albeit one that
involves -adic integration for infinitely many primes .
Our method of proof of the integral Gross--Stark conjecture is a
generalization of our previous work on the Brumer--Stark conjecture. We apply
Ribet's method in the context of group ring valued Hilbert modular forms. A key
new construction here is the definition of a Galois module \nabla_{\!\sL}
that incorporates an integral version of the Greenberg--Stevens \sL-invariant
into the theory of Ritter--Weiss modules. This allows for the reinterpretation
of Gross's conjecture as the vanishing of the Fitting ideal of
\nabla_{\!\sL}. This vanishing is obtained by constructing a quotient of
\nabla_{\!\sL} whose Fitting ideal vanishes using the Galois representations
associated to cuspidal Hilbert modular forms..Comment: 70 pages (to appear in Duke Math. J.
On the Root of Unity Ambiguity in a Formula for the Brumer--Stark Units
No full textWe prove a conjectural formula for the Brumer--Stark units. Dasgupta--Kakde
have shown the formula is correct up to a bounded root of unity. In this paper
we resolve the ambiguity in their result. We also remove an assumption from
Dasgupta--Kakde's result on the formula.Comment: 12 pages. This version proves a stronger result, dealing with the
ambiguity at
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