It has been proven by Serre, Larsen–Pink and Chin, that over a smooth curve over a finite
field, the monodromy groups of compatible semi-simple pure lisse sheaves have “the same” …

Let X be a smooth scheme over a nite eld of characteristic p. Consider the coecient objects
of locally constant rank on X in l-adic Weil cohomology: these are lisse Weil sheaves in étale …

For varieties over a perfect field of characteristic p, etale cohomology with Q_l-coefficients is
a Weil cohomology theory only when l is not equal to p; the corresponding role for l= p is …

Let $ U $ be a smooth affine curve over a number field $ K $ with a compactification $ X $
and let ${\mathbb {L}} $ be a rank $2 $, geometrically irreducible lisse $\overline {{\mathbb …

For varieties over a perfect field of characteristic p, étale cohomology with Q ℓ-coefficients is
a Weil cohomology theory only when ℓ≠ p; the corresponding role for ℓ= p is played by …

Parabolicity conjecture of F-isocrystals Page 1 Annals of Mathematics 198 (2023), 619–656
https://doi.org/10.4007/annals.2023.198.2.3 Parabolicity conjecture of F-isocrystals By Marco …

In this article we give a survey of the various forms of Berthelot's conjecture and some of the
implications between them. By proving some comparison results between push-forwards of …

Let $ X_0 $ be a smooth geometrically connected variety defined over a finite field $\mathbb
F_q $ and let $\mathcal E_0^{\dagger} $ be an irreducible overconvergent $ F $-isocrystal …

We formulate a conjectural analogue of Chebotar\" ev's density theorem for convergent $ F $-
isocrystals over a smooth geometrically irreducible curve defined over a finite field using the …

Let $ X $ be a smooth scheme over a finite field of characteristic $ p $. In answer to a
conjecture of Deligne, we establish that for any prime $\ell\neq p $, an $\ell $-adic Weil sheaf …