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Theory of weights in p-adic cohomology
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 140, Number 4, August 2018
- pp. 879-975
- 10.1353/ajm.2018.0021
- Article
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Abstract:
Let $k$ be a finite field of characteristic $p>0$. We construct a theory of weights for overholonomic complexes of arithmetic ${\cal D}$-modules with Frobenius structure on varieties over $k$. The notion of weight behave like Deligne's one in the $\ell$-adic framework: first, the six operations preserve weights, and secondly, the intermediate extension of an immersion preserves pure complexes and weights.