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Galois Module Structure Of Lubin Tate Modules
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Book Synopsis Galois Module Structure of Lubin-Tate Modules by : Sebastian Tomaskovic-Moore
Download or read book Galois Module Structure of Lubin-Tate Modules written by Sebastian Tomaskovic-Moore and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let L/K be a finite, Galois extension of local or global fields. In the classical setting of additive Galois modules, the ring of integers OL of L is studied as a module for the group ring OKG, where G is the Galois group of L/K. When K is a p-adic field, we also find a structure of OKG module when we replace OL with the group of points in OL of a Lubin-Tate formal group defined over K. For this new Galois module we find an analogue of the normal basis theorem. When K is a proper unramified extension of Qp , we show that some eigenspaces for the Teichmüller character are not free. We also adapt certain cases of E. Noether's result on normal integral bases for tame extensions. Finally, for wild extensions we define a version of Leopoldt's associated order and demonstrate in a specific case that it is strictly larger than the integral group ring.
Book Synopsis Relative Lubin-Tate Formal Groups and Galois Module Structure by : Chan Shih-Ping
Download or read book Relative Lubin-Tate Formal Groups and Galois Module Structure written by Chan Shih-Ping and published by . This book was released on 1990 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiplicative Galois Module Structure by : Alfred Weiss
Download or read book Multiplicative Galois Module Structure written by Alfred Weiss and published by American Mathematical Soc.. This book was released on 1996 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is the result of a short course on the Galois structure of S -units that was given at The Fields Institute in the autumn of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behaviour of Artin L -functions at s = 0. A proof of this - or even a precise formulation - is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of S -units can be described. This is intended for graduate students and research mathematicians, specifically algebraic number theorists.
Book Synopsis Galois Module Structure by : Victor Percy Snaith
Download or read book Galois Module Structure written by Victor Percy Snaith and published by American Mathematical Soc.. This book was released on 1994 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. This title addresses the Chinburg conjectures. It provides the background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions.
Book Synopsis Galois Representations and (Phi, Gamma)-Modules by : Peter Schneider
Download or read book Galois Representations and (Phi, Gamma)-Modules written by Peter Schneider and published by Cambridge University Press. This book was released on 2017-04-20 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.
Book Synopsis Hopf Algebras and Galois Module Theory by : Lindsay N. Childs
Download or read book Hopf Algebras and Galois Module Theory written by Lindsay N. Childs and published by American Mathematical Soc.. This book was released on 2021-11-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Book Synopsis Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules by : Laurent Berger
Download or read book Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules written by Laurent Berger and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cyclotomic means that Γ=Gal(Qp(μp∞)/Qp) is the Galois group of the cyclotomic extension of Qp. In order to generalize the p-adic local Langlands correspondence to GL2(L), where L is a finite extension of Qp, it seems necessary to have at our disposal a theory of Lubin-Tate (φ,Γ)-modules. Such a generalization has been carried out, to some extent, by working over the p-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic (φ,Γ)-modules in a different fashion. Instead of the p-adic open unit disk, the authors work over a character variety that parameterizes the locally L-analytic characters on oL. They study (φ,Γ)-modules in this setting and relate some of them to what was known previously.
Book Synopsis Algebraic Number Theory and Diophantine Analysis by : F. Halter-Koch
Download or read book Algebraic Number Theory and Diophantine Analysis written by F. Halter-Koch and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Publications mathématiques de Besançon N° 1/2010 by : Patrick Hild
Download or read book Publications mathématiques de Besançon N° 1/2010 written by Patrick Hild and published by Presses Univ. Franche-Comté. This book was released on 2010-03 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modular Functions, Elliptic Functions and Galois Module Structure by : S-P. Chan
Download or read book Modular Functions, Elliptic Functions and Galois Module Structure written by S-P. Chan and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abelian l-Adic Representations and Elliptic Curves by : Jean-Pierre Serre
Download or read book Abelian l-Adic Representations and Elliptic Curves written by Jean-Pierre Serre and published by CRC Press. This book was released on 1997-11-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Download or read book Manuscripta Mathematica written by and published by . This book was released on 1992 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Module Structure of Weakly Ramified Covers of Curves by : Sugil Lee
Download or read book Galois Module Structure of Weakly Ramified Covers of Curves written by Sugil Lee and published by . This book was released on 2020 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of our study is the obstruction to the existence of a normal integral basis for certain Galois modules of geometric origin. When G is a finite group acting on a projective scheme X over \\Spec Z and F is a G-equivariant coherent sheaf of O_X-modules, the sheaf cohomology groups H. i(X, \\F) are G-modules, and one asks if its equivariant Euler characteristic$$\\chi(X, F) := \\sum_i (-1). i [H. i(X, F)]$$can be calculated using a bounded complex of finitely generated free modules over Z[G]. Then we say that the cohomology of F has a normal integral basis. The obstruction to the existence of a normal integral basis has been of great interest in the classical case of number fields: As conjectured by Frohlich and proven by Taylor, when N/Q is a finite tamely ramified Galois extension with Galois group G, the Galois module structure of the ring of integers O_N is determined (up to stable isomorphism) by the root numbers appearing in the functional equations of Artin L-functions associated to symplectic representations of G. Chinburg started a generalization of the theory to some schemes with tame group actions by introducing the reduced projective Euler characteristic classes $\\overline{\\chi}. P(X, F)$.These Euler characteristics are elements of the class group $Cl(Z[G])$ and give the obstruction to the existence of normal integral basis.Our aim is to generalize the theory to the ``simplest'' kind of wild ramification, namely to weakly ramified covers of curves over Spec Z. If N/Q is wildly ramified, then O_N is not a free Z[G]-module. Erez showed that when the order |G| is odd, then the different ideal $\\frak{D}_{N/Q}$ is a square, and the square root of the inverse different is a locally free Z[G]-module if and only if N/Q is weakly ramified. Kock classified all fractional ideals of weakly ramified local rings that have normal integral bases. We generalize both of the results to curves over Spec Z to construct projective Euler characteristic for certain equivariant sheaves on weakly ramified covers of curves.
Book Synopsis Galois Extensions of Structured Ring Spectra by : John Rognes
Download or read book Galois Extensions of Structured Ring Spectra written by John Rognes and published by American Mathematical Soc.. This book was released on 2008-02-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.
Book Synopsis Homotopy Theory: Tools and Applications by : Daniel G. Davis
Download or read book Homotopy Theory: Tools and Applications written by Daniel G. Davis and published by American Mathematical Soc.. This book was released on 2019-05-30 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17–21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.
Book Synopsis Heegner Points and Rankin L-Series by : Henri Darmon
Download or read book Heegner Points and Rankin L-Series written by Henri Darmon and published by Cambridge University Press. This book was released on 2004-06-21 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.
