Rigid Analytic Uniformization of Hyperelliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rigid Analytic Uniformization of Hyperelliptic Curves write by Samuel Kadziela. This book was released on 2007. Rigid Analytic Uniformization of Hyperelliptic Curves available in PDF, EPUB and Kindle. We describe a method for approximating the Mumford curve model O/Gamma of a given totally split hyperelliptic curve y2 = i=12g+2x-a i . Once the generators of the Schottky group Gamma are obtained, we also explain how to use them to compute the period lattice of the Jacobian of the curve.
Rigid Analytic Geometry and Its Applications
Rigid Analytic Geometry and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rigid Analytic Geometry and Its Applications write by Jean Fresnel. This book was released on 2004. Rigid Analytic Geometry and Its Applications available in PDF, EPUB and Kindle. The theory of rigid (analytic) spaces, originally invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties, has undergone significant growth in the last two decades; today the theory has applications to arithmetic algebraic geometry, number theory, the arithmetic of function fields, and p -adic differential equations. This work, a revised and greatly expanded new English edition of the earlier French text by the same authors, is an accessible introduction to the theory of rigid spaces and now includes a large number of exercises. Key topics: * Chapters on the applications of this theory to curves and abelian varieties: the Tate curve, stable reduction for curves, Mumford curves, N??ron models, uniformization of abelian varieties * Unified treatment of the concepts: points of a rigid space, overconvergent sheaves, Monsky--Washnitzer cohomology and rigid cohomology; detailed examination of Kedlayaa??s application of the Monsky--Washnitzer cohomology to counting points on a hyperelliptic curve over a finite field * The work of Drinfeld on "elliptic modules" and the Langlands conjectures for function fields use a background of rigid ??tale cohomology; detailed treatment of this topic * Presentation of the rigid analytic part of Raynauda??s proof of the Abhyankar conjecture for the affine line, with only the rudiments of that theory A basic knowledge of algebraic geometry is a sufficient prerequisite for this text. Advanced graduate students and researchers in algebraic geometry, number theory, representation theory, and other areas of mathematics will benefit from the booka??s breadth and clarity.
Tropical and Non-Archimedean Geometry
Tropical and Non-Archimedean Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tropical and Non-Archimedean Geometry write by Omid Amini. This book was released on 2014-12-26. Tropical and Non-Archimedean Geometry available in PDF, EPUB and Kindle. Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to say about the other. This volume is a collection of articles dedicated to one or both of these disciplines. Some of the articles are based, at least in part, on the authors' lectures at the 2011 Bellairs Workshop in Number Theory, held from May 6-13, 2011, at the Bellairs Research Institute, Holetown, Barbados. Lecture topics covered in this volume include polyhedral structures on tropical varieties, the structure theory of non-Archimedean curves (algebraic, analytic, tropical, and formal), uniformisation theory for non-Archimedean curves and abelian varieties, and applications to Diophantine geometry. Additional articles selected for inclusion in this volume represent other facets of current research and illuminate connections between tropical geometry, non-Archimedean geometry, toric geometry, algebraic graph theory, and algorithmic aspects of systems of polynomial equations.
Rigid Analytic Geometry and Its Applications
Rigid Analytic Geometry and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Rigid Analytic Geometry and Its Applications write by Jean Fresnel. This book was released on 2012-12-06. Rigid Analytic Geometry and Its Applications available in PDF, EPUB and Kindle. Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.
Note on the Uniformization of Hyperelliptic Curves
Note on the Uniformization of Hyperelliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Note on the Uniformization of Hyperelliptic Curves write by Jonathan Hodgkinson. This book was released on 1936. Note on the Uniformization of Hyperelliptic Curves available in PDF, EPUB and Kindle.
