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Perfectoid Spaces

Lectures from the 2017 Arizona Winter School

By: Bhargav Bhatt,Ana Caraiani,Kiran S. Kedlaya,Peter Scholze,Jared Weinstein

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Perfectoid Spaces

Lectures from the 2017 Arizona Winter School

By: Bhargav Bhatt,Ana Caraiani,Kiran S. Kedlaya,Peter Scholze,Jared Weinstein

Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic $p$, and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. In recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2018. This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad introduction to the subject. After an introduction with insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a user-friendly and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the foundational material, studies vector bundles on Fargues–Fontaine curves, and introduces diamonds and shtukas over them with a view toward the local Langlands correspondence. Bhargav Bhatt explains the application of perfectoid spaces to comparison isomorphisms in $p$-adic Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction of Galois representations associated to torsion classes in the cohomology of locally symmetric spaces for the general linear group. This book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.

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Page Count

297

Publisher

American Mathematical Society

Published Date

ISBN 10

1470465108

ISBN 13

9781470465100

Being Hindu, Being Indian

Lala Lajpat Rai’s Ideas of Nationhood

By: Vanya Vaidehi Bhargav

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Being Hindu, Being Indian

Lala Lajpat Rai’s Ideas of Nationhood

By: Vanya Vaidehi Bhargav

In popular imagination, Lala Lajpat Rai is frequently associated with Bhagat Singh, who, by assassinating J.P. Saunders, avenged Rai’s death, caused by a police lathi charge, and was hanged for it. Lajpat Rai is also remembered for his fervent opposition to British rule. In recent decades, however, historians have converged with the Hindu Right in rediscovering Lajpat Rai as an ideological ancestor of Hindutva. But what then explains Rai’s wholehearted approval of Congress–Muslim League cooperation, and attempt to endow Hindus and Muslims with bonds of common belonging? Why did he reinterpret India’s medieval history to highlight peaceful coexistence between Hindus and Muslims? Have our hasty conclusions about Lajpat Rai’s nationalist thought concealed its complexities and distorted our understanding of nationalism in general? Meticulously researched and eloquently written, Being Hindu, Being Indian offers the first comprehensive examination of Lajpat Rai’s nationalist thought. By revealing the complexities of Rai’s thinking, it provokes us to think more deeply about broader questions relevant to present-day politics: Are all expressions of ‘Hindu nationalism’ the same as Hindutva? What are the similarities and differences between ‘Hindu’ and ‘Indian’ nationalism? Can communalism and secularism be expressed together? How should we understand fluidity in politics? This book invites readers to treat Lajpat Rai’s ideas as a gateway to think more deeply about history, politics, religious identity and nationhood.

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Page Count

482

Publisher

Penguin Random House India Private Limited

Published Date

ISBN 10

9357085831

ISBN 13

9789357085830