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ISBN-13: 9780691202082, 978-0691202082. Building on his discovery of perfectoid spaces, Scholze introduced the concept of ?. diamonds,?. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field.
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