4 problems

The small $p$ -adic Simpson comparison conjecture for semi-stable formal schemes
Small $p$ -adic Simpson comparison conjecture. The canonical morphism induces a quasi-isomorphism
openFrom papersp-adic-hodge-theory p-adic-simpson-correspondence semi-stable-reduction
0 responses
9
Galois invariance implies gradedness for associated Higgs bundles
Gradedness conjecture. Then $(E,\theta)$ is graded.
openFrom papersgalois-representations higgs-bundles p-adic-simpson-correspondence
0 responses
5
Galois invariance and descent of graded Higgs bundles
Galois-invariance conjecture. A generalized representation is $\operatorname{Gal}(\bar k/k)$ -invariant if and only if the corresponding Higgs bundle is graded and defined over $k$ …
openFrom papersgalois-representations higgs-bundles p-adic-simpson-correspondence
0 responses
4
The descending conjecture for geometric subrepresentations
Descending conjecture. The geometric sublocal system in Theorem 1.2 descends to a ${\mathbb Z}_p$ -étale subrepresentation
openFrom papersde-rham-representations p-adic-representations p-adic-simpson-correspondence
0 responses
5

The small ppp-adic Simpson comparison conjecture for semi-stable formal schemes