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Shafarevich Seminar
July 7, 2020 15:00, Moscow, online
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A $p$-adic Riemann-Hilbert functor and applications
B. Bhatt |
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This page: | 380 |
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Abstract:
Perverse sheaves on complex algebraic varieties have some
remarkable rigidity properties. When translated through the
Riemann-Hilbert correspondence, these can often (e.g., via the
theory of Hodge modules) lead to highly non-trivial vanishing
theorems on the cohomology of coherent sheaves. I'll explain ongoing
work (joint with Jacob Lurie) on a Riemann-Hilbert functor for
perverse sheaves on algebraic varieties over a p-adic field. When
applied to $Q_p$-sheaves, this allows us to recover some of the
aforementioned vanishing theorems. Moreover, unlike the complex
variant, our functor also makes sense for $F_p$-sheaves, which leads
to new vanishing theorems in mixed characteristic algebraic
geometry.
Language: English
Website:
https://us02web.zoom.us/j/83327069709
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