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Prismatic F-crystals and E-crystalline Galois representations

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The equivalence between prismatic f-crystals and e-crystalline Galois representations is established.
A general full faithfulness result for vector bundles on the prismatic site is proven.
This work refines Bhatt–Scholze's approach by avoiding the Beilinson fibre sequence.
The setting involves a complete discretely valued field with a perfect residue field.

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This analysis shows the equivalence of prismatic f-crystals and e-crystalline Galois representations, pointing to a new insight on vector bundles.

Duc Truong Pham (2025) studied this question.

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This analysis shows the equivalence of prismatic f-crystals and e-crystalline Galois representations, pointing to a new insight on vector bundles.