Arithmetic and Geometry

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The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on

Automorphic Forms Beyond $mathrm {GL}_2$

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The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representa

Arithmetic Compactifications of PEL-Type Shimura Varieties

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By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimur

Arithmetic Compactifications of PEL-type Shimura Varieties

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By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimur

Perfectoid Spaces

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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 man