Compactification Of The Drinfeld Modular Surfaces
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Compactification Of The Drinfeld Modular Surfaces
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Author : Thomas Lehmkuhl
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-01-21
Compactification Of The Drinfeld Modular Surfaces written by Thomas Lehmkuhl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-21 with Science categories.
In this article the author describes in detail a compactification of the moduli schemes representing Drinfeld modules of rank 2 endowed with some level structure. The boundary is a union of copies of moduli schemes for Drinfeld modules of rank 1, and its points are interpreted as Tate data. The author also studies infinitesimal deformations of Drinfeld modules with level structure.
Drinfeld Modules
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Author : Mihran Papikian
language : en
Publisher: Springer Nature
Release Date : 2023-03-31
Drinfeld Modules written by Mihran Papikian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-31 with Mathematics categories.
This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.
Arithmetic Geometry Over Global Function Fields
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Author : Gebhard Böckle
language : en
Publisher: Springer
Release Date : 2014-11-13
Arithmetic Geometry Over Global Function Fields written by Gebhard Böckle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Mathematics categories.
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.
Compactifications Of Symmetric And Locally Symmetric Spaces
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Author : Armand Borel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-25
Compactifications Of Symmetric And Locally Symmetric Spaces written by Armand Borel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-25 with Mathematics categories.
Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology
Banach Algebras On Semigroups And On Their Compactifications
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Author : Harold G. Dales
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Banach Algebras On Semigroups And On Their Compactifications written by Harold G. Dales and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 205, number 966 (end of volume)."
Number Fields And Function Fields Two Parallel Worlds
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Author : Gerard B. M. van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-24
Number Fields And Function Fields Two Parallel Worlds written by Gerard B. M. van der Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-24 with Mathematics categories.
Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections
Yang Mills Connections On Orientable And Nonorientable Surfaces
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Author : Nan-Kuo Ho
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-08
Yang Mills Connections On Orientable And Nonorientable Surfaces written by Nan-Kuo Ho and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-08 with Mathematics categories.
In ``The Yang-Mills equations over Riemann surfaces'', Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In ``Yang-Mills Connections on Nonorientable Surfaces'', the authors study Yang-Mills functional on the space of connections on a principal $G_{\mathbb{R}}$-bundle over a closed, connected, nonorientable surface, where $G_{\mathbb{R}}$ is any compact connected Lie group. In this monograph, the authors generalize the discussion in ``The Yang-Mills equations over Riemann surfaces'' and ``Yang-Mills Connections on Nonorientable Surfaces''. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.
The Recognition Theorem For Graded Lie Algebras In Prime Characteristic
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Author : Georgia Benkart
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
The Recognition Theorem For Graded Lie Algebras In Prime Characteristic written by Georgia Benkart and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
"Volume 197, number 920 (second of 5 numbers)."
Center Manifolds For Semilinear Equations With Non Dense Domain And Applications To Hopf Bifurcation In Age Structured Models
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Author : Pierre Magal
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Center Manifolds For Semilinear Equations With Non Dense Domain And Applications To Hopf Bifurcation In Age Structured Models written by Pierre Magal and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.
Hypocoercivity
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Author : Cdric Villani
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-08
Hypocoercivity written by Cdric Villani and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-08 with Mathematics categories.
This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, taking the general form ${\frac{\partial f}{\partial t}}+ L f =0$. The question is whether and how one can overcome the degeneracy by exploiting commutators.