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p-adic periods via perfectoid spaces

Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017

March 31, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Kiran Kedlaya (University of California, San Diego)
Location: MSRI: Simons Auditorium
  • Galois theory

  • Galois orbits

  • Periods

  • cohomology comparison theorems

  • p-adic cohomology

  • perfectoid spaces

  • crystalline comparison theorem

  • crystalline cohomology

  • motives

  • Shimura varieties

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



Given the interpretation of classical periods as matrix coefficients arising in the comparison between singular and de Rham cohomology of complex algebraic varieties, it is natural to view as a p-adic analogue the comparison between etale, crystalline, and de Rham cohomology of algebraic varieties. We describe some new results and perspectives on p-adic comparison isomorphisms emerging from recent developments in the theory of perfectoid spaces. These include a new direct cohomological realization of the crystalline comparison isomorphism (by Bhatt-Morrow-Scholze), and the discovery of "abstract instances" of comparison isomorphisms corresponding to as-yet-unknown families of motives over Shimura varieties (by Liu-Zhu).

28378?type=thumb Kedlaya.Notes 776 KB application/pdf Download
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