Prof. Dr. Peter Scholze Director of the Max Planck Institute for Mathematics |
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Academic Career | |||||||||||||||||||||||||||||||
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Awards | |||||||||||||||||||||||||||||||
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Invited Lectures | |||||||||||||||||||||||||||||||
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Editorships | |||||||||||||||||||||||||||||||
• Journal of the AMS
• Compositio Math |
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Research Profile | |||||||||||||||||||||||||||||||
My research is at the intersection of number theory and algebraic geometry, and deals with the basic questions and structures that underly our modern understanding of diophantine equations. This concerns on the one hand the Langlands program, which connects objects from arithmetic geometry, such as elliptic curves over number fields, with analytic or topological objects, such as modular forms or the cohomology of hyperbolic manifolds. On the other hand, this concerns the cohomological invariants attached to arithmetic varieties themselves, which forms the subject of Hodge theory, or more particularly p-adic Hodge theory.
My own contributions to these questions include the construction of Galois representations associated for example with torsion classes on hyperbolic 3-manifolds, and the development of a geometric framework underlying much of p-adic Hodge theory, in the form of perfectoid spaces. In the future, I plan to pursue these questions. In particular, building on perfectoid spaces, I want to transport some machinery from the geometric Langlands program to the case of p-adic fields, and I hope to use this to obtain new results on the local Langlands conjecture for general groups over p-adic fields. On the other hand, in work with Bhatt and Morrow, we found new cohomological invariants of arithmetic varieties, which lead to a surprising q-deformation of de Rham cohomology, which I plan to study further. |
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Selected Publications | |||||||||||||||||||||||||||||||
[1] Bhargav Bhatt, Peter Scholze Projectivity of the Witt vector affine Grassmannian Invent. Math. , 209: (2): 329--423 2017 DOI: 10.1007/s00222-016-0710-4 [2] Peter Scholze On torsion in the cohomology of locally symmetric varieties Ann. of Math. (2) , 182: (3): 945--1066 2015 DOI: 10.4007/annals.2015.182.3.3 [3] Bhargav Bhatt, Peter Scholze The pro-étale topology for schemes Astérisque (369): 99--201 2015 ISBN: 978-2-85629-805-3 [4] Peter Scholze, Jared Weinstein Moduli of p-divisible groups Camb. J. Math. , 1: (2): 145--237 2013 DOI: 10.4310/CJM.2013.v1.n2.a1 [5] Peter Scholze p-adic Hodge theory for rigid-analytic varieties Forum Math. Pi , 1: : e1, 77 2013 DOI: 10.1017/fmp.2013.1 [6] Peter Scholze The local Langlands correspondence for GLn over p-adic fields Invent. Math. , 192: (3): 663--715 2013 DOI: 10.1007/s00222-012-0420-5 [7] Peter Scholze, Sug Woo Shin On the cohomology of compact unitary group Shimura varieties at ramified split places J. Amer. Math. Soc. , 26: (1): 261--294 2013 DOI: 10.1090/S0894-0347-2012-00752-8 [8] Peter Scholze Perfectoid spaces Publ. Math. Inst. Hautes �tudes Sci. , 116: : 245--313 2012 DOI: 10.1007/s10240-012-0042-x [9] Ana Caraiani, Peter Scholze
On the generic part of the cohomology of compact unitary Shimura varieties Ann. of Math. (2) , 186: (3): 649--766 2017 DOI: 10.4007/annals.2017.186.3.1 |
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Publication List |