A p-adic Simpson correspondence for rigid analytic varieties
Y Wang - Algebra & Number Theory, 2023 - msp.org
Algebra & Number Theory, 2023•msp.org
We establish a p-adic Simpson correspondence in the spirit of Liu and Zhu for rigid analytic
varieties X over ℂ p with a liftable good reduction by constructing a new period sheaf on X
proét. To do so, we use the theory of cotangent complexes described by Beilinson and Bhatt.
Then we give an integral decompletion theorem and complete the proof by local
calculations. Our construction is compatible with the previous works of Faltings and Liu and
Zhu.
varieties X over ℂ p with a liftable good reduction by constructing a new period sheaf on X
proét. To do so, we use the theory of cotangent complexes described by Beilinson and Bhatt.
Then we give an integral decompletion theorem and complete the proof by local
calculations. Our construction is compatible with the previous works of Faltings and Liu and
Zhu.
Abstract
We establish a p-adic Simpson correspondence in the spirit of Liu and Zhu for rigid analytic varieties X over ℂ p with a liftable good reduction by constructing a new period sheaf on X proét. To do so, we use the theory of cotangent complexes described by Beilinson and Bhatt. Then we give an integral decompletion theorem and complete the proof by local calculations. Our construction is compatible with the previous works of Faltings and Liu and Zhu.
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