1.

Record Nr.

UNISALENTO991002945499707536

Titolo

Berkovich spaces and applications [e-book] / Antoine Ducros, Charles Favre, Johannes Nicaise, editors

Pubbl/distr/stampa

Cham [Switzerland] : Springer, 2015

ISBN

9783319110295

Descrizione fisica

1 online resource (xix, 413 pages)

Collana

Lecture Notes in Mathematics, 1617-9692 ; 2119

Classificazione

AMS 14-06

AMS 14F20

AMS 14G22

LC QA551

Altri autori (Persone)

Ducros, Antoineauthor

Favre, Charlesauthor

Nicaise, Johannesauthor

Disciplina

516.35

Soggetti

Geometry, Analytic

Topology

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references

Nota di contenuto

Introduction to Berkovich analytic spaces -- Etale cohomology of schemes and analytic spaces -- Countability properties of Berkovich spaces -- Cohomological finiteness of proper morphisms in algebraic geometry: a purely transcendental proof, without projective tools -- Bruhat-Tits buildings and analytic geometry -- Dynamics on Berkovich spaces in low dimensions -- Compactifications of spaces of representations (after Culler, Morgan and Shalen)

Sommario/riassunto

We present an introduction to Berkovich?s theory of non-archimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of



Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory of compactification of character varieties. This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to discover new settings where these beautiful and intricate objects might arise

2.

Record Nr.

UNINA9910420930303321

Autore

Miller Larry Benjamin

Titolo

Islamic Disputation Theory : The Uses & Rules of Argument in Medieval Islam / / by Larry Benjamin Miller

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020

ISBN

3-030-45012-0

Edizione

[1st ed. 2020.]

Descrizione fisica

1 online resource (xviii, 143 pages)

Collana

Logic, Argumentation & Reasoning, Interdisciplinary Perspectives from the Humanities and Social Sciences, , 2214-9120 ; ; 21

Disciplina

297.209

Soggetti

Philosophy, Medieval

Law

Philology

Medieval Philosophy

Law, general

Classical Studies

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

1. Theological Dialectic (Jadal) -- 2. Dialectic and Arabic Philosophy -- 3. Dialectic (Jadal) in Jurisprudence -- 4. The Ādāb Al-Baḥth.

Sommario/riassunto

This book charts the evolution of Islamic dialectical theory (jadal) over a four-hundred year period. It includes an extensive study of the



development of methods of disputation in Islamic theology (kalām) and jurisprudence (uṣūl al-fiqh) from the tenth through the fourteenth centuries. The author uses the theoretical writings of Islamic theologians, jurists, and philosophers to describe the concept Overall, this investigation looks at the extent to which the development of Islamic modes of disputation is rooted in Aristotle and the classical tradition. The author reconstructs the contents of the earliest systematic treatment of the subject by b. al-Rīwandī. He then contrasts the theological understanding of dialectic with the teachings of the Arab Aristotelians–al-Fārābī, Avicenna, and Averroes. Next, the monograph shows how jurists took over the theological method of dialectic and applied it to problems peculiar to jurisprudence. Although the earliest writings on dialectic are fairly free of direct Aristotelian influence, there are coincidences of themes and treatment. But after jurisprudence had assimilated the techniques of theological dialectic, its own theory became increasingly influenced by logical terminology and techniques. At the end of the thirteenth century there arose a new discipline, the ādāb al-baḥth. While the theoretical underpinnings of the new system are Aristotelian, the terminology and order of debate place it firmly in the Islamic tradition of disputation.