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Prismatic and p-de Rham cohomology: comparison theorems and antecedents

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Title
Prismatic and p-de Rham cohomology: comparison theorems and antecedents
Alternative Title
Prisms, prismatic neighborhoods, and p-de Rham cohomology
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10
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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Release Date2021
LanguageEnglish

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Abstract
Prismatic cohomology, as proposed by B. Bhatt and P. Scholze, provides a uniform framework for many of the cohomoogy theories involved in p-adic Hodge theory. I will focus on the crystalline incarnation of prismatic cohomology and its relation to p-de Rham cohomology, as suggested by B. Bhatt. I will also attempt to relate crystalline prisms to previoius work on the p-adic Cartier transform due to several authors. The main new ingredient is a detailed study of the geometry of Frobenius lifts and prismatic neighborhoods.