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Perfectoid Spaces - Lectures from the 2017 Arizona Winter School (Paperback)
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Perfectoid Spaces - Lectures from the 2017 Arizona Winter School (Paperback)
Series: Mathematical Surveys and Monographs
Expected to ship within 10 - 15 working days
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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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