Geometric Aspects Of Dwork Theory

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Geometric Aspects Of Dwork Theory

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Author : Alan Adolphson
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22

Geometric Aspects Of Dwork Theory written by Alan Adolphson and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.

This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on the geometric applications of the p-adic analytic techniques originating in Dwork's work, their connection to various recent cohomology theories and to modular forms. The two volumes contain both important new research and illuminating survey articles written by leading experts in the field. The book will provide an indispensable resource for all those wishing to approach the frontiers of research in arithmetic algebraic geometry.

Geometric Aspects Of Dwork Theory

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Author : Alan Adolphson
language : en
Publisher: Walter de Gruyter
Release Date : 2004

Geometric Aspects Of Dwork Theory written by Alan Adolphson and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Geometry, Algebraic categories.

Commutative Algebra And Noncommutative Algebraic Geometry

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Author : David Eisenbud
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-19

Commutative Algebra And Noncommutative Algebraic Geometry written by David Eisenbud and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-19 with Mathematics categories.

This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

Nonarchimedean And Tropical Geometry

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Author : Matthew Baker
language : en
Publisher: Springer
Release Date : 2016-08-18

Nonarchimedean And Tropical Geometry written by Matthew Baker and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-18 with Mathematics categories.

This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.

Geometry And Dynamics Of Groups And Spaces

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Author : Mikhail Kapranov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-05

Geometry And Dynamics Of Groups And Spaces written by Mikhail Kapranov 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 2008-03-05 with Mathematics categories.

Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Algebraic Theory Of Differential Equations

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Author :
language : en
Publisher: Cambridge University Press
Release Date :

Algebraic Theory Of Differential Equations written by and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Perspectives On Four Decades Of Algebraic Geometry Volume 1

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Author : Alberto Albano
language : en
Publisher: Springer Nature
Release Date : 2025-01-22

Perspectives On Four Decades Of Algebraic Geometry Volume 1 written by Alberto Albano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-22 with Mathematics categories.

The first of a two-part volume, this collection offers a unifying vision of algebraic geometry, exploring its evolution over the last four decades as well as state-of-the art research. With chapters written by established leaders in the field as well as younger researchers, readers will gain a wide-ranging perspective of the area. The volume also commemorates the significant talent and contributions of Alberto Collino, whose scientific accomplishments helped shape the themes and topics covered. Perspectives on Four Decades of Algebraic Geometry, Volume 1 will be a valuable resource for those interested in the ways algebraic geometry has expanded over the years and continues to grow. "Quadratic Counts of Twisted Cubics" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

P Adic Aspects Of Modular Forms

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Author : Baskar Balasubramanyam
language : en
Publisher: World Scientific
Release Date : 2016-06-14

P Adic Aspects Of Modular Forms written by Baskar Balasubramanyam and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-14 with Mathematics categories.

The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n).

Arakelov Geometry Over Adelic Curves

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Author : Huayi Chen
language : en
Publisher: Springer Nature
Release Date : 2020-01-29

Arakelov Geometry Over Adelic Curves written by Huayi Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-29 with Mathematics categories.

The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions. By adelic curve is meant a field equipped with a family of absolute values parametrized by a measure space, such that the logarithmic absolute value of each non-zero element of the field is an integrable function on the measure space. In the literature, such construction has been discussed in various settings which are apparently transversal to each other. The authors first formalize the notion of adelic curves and discuss in a systematic way its algebraic covers, which are important in the study of height theory of algebraic points beyond Weil–Lang’s height theory. They then establish a theory of adelic vector bundles on adelic curves, which considerably generalizes the classic geometry of vector bundles or that of Hermitian vector bundles over an arithmetic curve. They focus on an analogue of the slope theory in the setting of adelic curves and in particular estimate the minimal slope of tensor product adelic vector bundles. Finally, by using the adelic vector bundles as a tool, a birational Arakelov geometry for projective variety over an adelic curve is developed. As an application, a vast generalization of Nakai–Moishezon’s criterion of positivity is proven in clarifying the arguments of geometric nature from several fundamental results in the classic geometry of numbers. Assuming basic knowledge of algebraic geometry and algebraic number theory, the book is almost self-contained. It is suitable for researchers in arithmetic geometry as well as graduate students focusing on these topics for their doctoral theses.

Noncommutative Geometry And Physics Proceedings Of The Coe International Workshop

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Author : Naoya Miyazaki
language : en
Publisher: World Scientific
Release Date : 2005-09-23

Noncommutative Geometry And Physics Proceedings Of The Coe International Workshop written by Naoya Miyazaki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-23 with Mathematics categories.

Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a variety of mathematical areas related to noncommutative geometry and its interface with modern theoretical physics.