The Dynamical Mordell-Lang Conjecture for Polynomial Endomorphisms of the Affine Plane

The Dynamical Mordell-Lang Conjecture for Polynomial Endomorphisms of the Affine Plane
Author :
Publisher :
Total Pages : 110
Release :
ISBN-10 : 2856298699
ISBN-13 : 9782856298695
Rating : 4/5 (99 Downloads)

Synopsis The Dynamical Mordell-Lang Conjecture for Polynomial Endomorphisms of the Affine Plane by : Junyi Xie

In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane over the algebraic numbers. More precisely, let f be an endomorphism of the affine plan over the algebraic numbers. Let x be a point in the affine plan and C be a curve. If the intersection of C and the orbits of x is infinite, then C is periodic.

The Dynamical Mordell–Lang Conjecture

The Dynamical Mordell–Lang Conjecture
Author :
Publisher : American Mathematical Soc.
Total Pages : 297
Release :
ISBN-10 : 9781470424084
ISBN-13 : 1470424088
Rating : 4/5 (84 Downloads)

Synopsis The Dynamical Mordell–Lang Conjecture by : Jason P. Bell

The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point x under the action of an endomorphism f of a quasiprojective complex variety X. More precisely, it claims that for any point x in X and any subvariety V of X, the set of indices n such that the n-th iterate of x under f lies in V is a finite union of arithmetic progressions. In this book the authors present all known results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a p-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.

A Torsion Jacquet-Langlands Correspondence

A Torsion Jacquet-Langlands Correspondence
Author :
Publisher :
Total Pages : 244
Release :
ISBN-10 : UCSD:31822044287571
ISBN-13 :
Rating : 4/5 (71 Downloads)

Synopsis A Torsion Jacquet-Langlands Correspondence by : Frank Calegari

"We prove a numerical form of a Jacquet-Langlands correspondence for torsion classes on arithmetic hyperbolic 3-manifolds." -- Prové de l'editor.

A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs

A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs
Author :
Publisher :
Total Pages : 148
Release :
ISBN-10 : UCSD:31822042539635
ISBN-13 :
Rating : 4/5 (35 Downloads)

Synopsis A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs by : Huanchen Bao

We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satsify a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical bases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BGG category [O] of the orthosymplectic Lie superalgebras osp(2m + 1[vertical bar]2n). In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.

Séminaire Bourbaki

Séminaire Bourbaki
Author :
Publisher :
Total Pages : 604
Release :
ISBN-10 : UCSD:31822044543536
ISBN-13 :
Rating : 4/5 (36 Downloads)

Synopsis Séminaire Bourbaki by : Société mathématique de France

"This 69th volume of the Bourbaki Seminar contains the texts of the fifteen survey lectures done during the year 2016/2017. Topics addressed covered Langlands correspondence, NIP property in model theory, Navier-Stokes equation, algebraic and complex analytic geometry, algorithmic and geometric questions in knot theory, analytic number theory formal moduli problems, general relativity, sofic entropy, sphere packings, subriemannian geometry." -- Prové de l'editor.

The Arithmetic of Elliptic Curves

The Arithmetic of Elliptic Curves
Author :
Publisher : Springer Science & Business Media
Total Pages : 414
Release :
ISBN-10 : 9781475719208
ISBN-13 : 1475719205
Rating : 4/5 (08 Downloads)

Synopsis The Arithmetic of Elliptic Curves by : Joseph H. Silverman

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Introduction to Toric Varieties

Introduction to Toric Varieties
Author :
Publisher : Princeton University Press
Total Pages : 174
Release :
ISBN-10 : 0691000492
ISBN-13 : 9780691000497
Rating : 4/5 (92 Downloads)

Synopsis Introduction to Toric Varieties by : William Fulton

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.

Mathematical Conversations

Mathematical Conversations
Author :
Publisher : Springer Science & Business Media
Total Pages : 486
Release :
ISBN-10 : 9781461301950
ISBN-13 : 1461301955
Rating : 4/5 (50 Downloads)

Synopsis Mathematical Conversations by : Robin Wilson

Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.

Arithmetic Differential Equations

Arithmetic Differential Equations
Author :
Publisher : American Mathematical Soc.
Total Pages : 346
Release :
ISBN-10 : 9780821838624
ISBN-13 : 0821838628
Rating : 4/5 (24 Downloads)

Synopsis Arithmetic Differential Equations by : Alexandru Buium

For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry
Author :
Publisher : Springer Science & Business Media
Total Pages : 700
Release :
ISBN-10 : 9780817647476
ISBN-13 : 0817647473
Rating : 4/5 (76 Downloads)

Synopsis Algebra, Arithmetic, and Geometry by : Yuri Tschinkel

EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.