p-adic periods via perfectoid spaces
Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017
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
14C30 - Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
11F85 - $p$-adic theory, local fields [See also 14G20, 22E50]
14F20 - Étale and other Grothendieck topologies and (co)homologies
Kedlaya
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).
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Kedlaya
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