Last edited by Mazulkree
Sunday, August 2, 2020 | History

5 edition of Galois Theory and Modular Forms (Developments in Mathematics) found in the catalog.

Galois Theory and Modular Forms (Developments in Mathematics)

  • 154 Want to read
  • 4 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Algebraic geometry,
  • Fields & rings,
  • Group Theory,
  • Forms, Modular,
  • Mathematics,
  • Science/Mathematics,
  • Algebra - General,
  • Geometry - Algebraic,
  • Mathematics / Algebra / General,
  • Mathematics-Geometry - Algebraic,
  • Mathematics-Group Theory,
  • Research,
  • Galois theory

  • Edition Notes

    ContributionsKi-ichiro Hashimoto (Editor), Katsuya Miyake (Editor), Hiroaki Nakamura (Editor)
    The Physical Object
    FormatHardcover
    Number of Pages406
    ID Numbers
    Open LibraryOL8372843M
    ISBN 101402076894
    ISBN 109781402076893

    Mathematics B Topics in Number Theory Modular forms and their Galois representations. Winter Quarter Haruzo HIDA. Meeting Time: Regularly Mondays and Wednesdays pm to pm in MS and Fridays either pm to pm or pm to pm in MS (Friday meeting time will be announced in the class before the meeting day). Lecture Starts on . CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this course, assuming basic knowledge of algebraic number theory, commutative algebra and topology, we study non-archimedean deformation theory of modular forms on GL(2) and modular Galois representations into GL(2). We plan to discuss the following four topics: (1) analytic/algebraic .

    The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. ical forms for matrices. These topics are covered in a standard graduate-level algebra course. I develop the properties of algebraic integers, valuation theory and completions within the text since they usually fall outside such a course. Many people have read sections of this book, worked through the exercises and beenFile Size: 1MB.

    Abstract: This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost all cases, be computed in polynomial time in the weight and the size of the finite field. modular forms using Dirichlet characters, and then explain how to compute a basis of Hecke eigenforms for each subspace using several approaches. We also discuss congruences between modular forms and bounds needed to provably generate the Hecke algebra. Chapter 10 is about computing analytic invariants of modular Size: 2MB.


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Galois Theory and Modular Forms (Developments in Mathematics) Download PDF EPUB FB2

In September,an international conference "Galois Theory Galois Theory and Modular Forms book Modular Forms" was held at Tokyo Metropolitan University after some preparatory work­ shops and symposia in previous years.

The title of this book came from that of the conference, and the authors were participants of those meet­ All of the articles here were critically. ISBN: OCLC Number: Description: xi, pages: illustrations ; 25 cm. Contents: The arithmetic of Weierstrass points on modular curves X[subscript 0](p) / Scott Ahlgren --Semistable abelian varieties with small division fields / Armand Brumer and Kenneth Kramer --Q-curves with rational j-invariants and jacobian surfaces of GL[subscript 2].

Get this from a library. Galois theory and modular forms. [K Hashimoto; Katsuya Miyake; Hiroaki Nakamura;] -- The key words for the book are "Galois groups", or more precisely "generic polynomials", "Galois coverings of algebraic curves" and "Shimura varieties".

The work includes surveys on branches of. Buy Galois Theory and Modular Forms (Developments in Mathematics) on FREE SHIPPING on qualified orders Galois Theory and Modular Forms (Developments in Mathematics): Ki-ichiro Hashimoto: : BooksCited by: 8.

$\begingroup$ You can try Diamond and Shurman's book "A First Course in Modular Forms". Galois rep-s are covered in the last chapter. Galois rep-s are covered in the last chapter.

If you find it hard, you can try Goldfeld and Hundley's "Automorphic Representations and L-Functions for the General Linear Group". Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices.

Their Fourier coefficients, with Ramanujan’s tau-function as a typical example, have deep arithmetic significance. In September,an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work­ shops and symposia in previous years.

The title of this book came from that of the conference, and the authors were participants of those meet­ All of the articles here were critically Format: Hardcover. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, - Selection from Computational Aspects of Modular Forms and Galois Representations [Book].

Galois theory allows one to reduce certain problems in field theory, especially those related to field extensions, to problems in group theory. (field-theory) tag instead.

For questions about abstractions of Galois theory, use (galois-connections). galois-theory elliptic-curves modular-forms. asked May 6 at rogerl. k 3 3 gold. This is a book about computational aspects of modular forms and the Galois representations attached to them.

The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost all cases, be computed in polynomial time in the weight and the size of the finite field.

Modular Functions and Modular Forms. pdf current version () Abstract This is an introduction to the arithmetic theory of modular functions and modular forms, with a greater emphasis on the geometry than most accounts. MODULAR FORMS AND THEIR GALOIS REPRESENTATIONS 2 number theory, DP/(p) is isomorphic to Gal(Qp/Qp) for the p-adic field Qp and its alge- braic closure σ∈DP induces an automorphism of Z/P which is an algebraic closure Fp of Fp, we have an exat sequence of compact groups 1 →IP/p →DP/p →Gal(Fp/Fp) →1.

for Fp = OF /p. Thus there is. This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat’s last theorem. Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a.

The Paperback of the Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau Due to COVID, orders may be delayed.

Thank you for your : Bas Edixhoven. The two main topics of this book are Iwasawa theory and modular forms. The presentation of the theory of modular forms starts with several beautiful relations discovered by Ramanujan and leads to a discussion of several important ingredients, including the zeta-regularized products, Kronecker's limit formula, and the Selberg trace formula.

Read "Computational Aspects of Modular Forms and Galois Representations How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM)" by Robin de Jong available from Rakuten Kobo.

Modular forms are tremendously important in various areas of mathematics, from number theoryBrand: Princeton University Press. This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem.

Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a substantial simplification of the Taylor. $\begingroup$ Dear David: A hint of the interaction with rep'n theory is already seen in the fact that the classical upper half-plane is a coset space for the Lie group ${\rm{GL}}_2(\mathbf{R})$, and relation of C-R eqns with Casimir in Lie alg., but need a more adelic formulation to see how the Hecke theory comes out from the action of a group also.

(Toy version: adelic formulation. In this chapter we explicitly compute mod-ℓ Galois representations attached to modular forms. To be precise, we look at cases with ℓ ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to We present the result in terms of polynomials associated with the projectivized representations.

This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem. Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a Price: $This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 thro at Boston University.

Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic .This is an introduction to the arithmetic theory of modular functions and modular forms, with a greater emphasis on the geometry than most accounts.

Elliptic Curves This course is an introductory overview of the topic including some of the work leading up to Wiles's proof of the Taniyama conjecture for most elliptic curves and Fermat's Last.