We prove a duality theorem for the $ p $-adic etale motivic cohomology of a variety $ U $
which is the complement of a divisor on a smooth projective variety over $\F_p $. This …

In order to study $ p $-adic étale cohomology of an open subvariety $ U $ of a smooth
proper variety $ X $ over a perfect field of characteristic $ p> 0$, we introduce new $ p …

We show that for a field k of characteristic p, H i (k, ℤ (n)) is uniquely p-divisible for i≠ n (we
use higher Chow groups as our definition of motivic cohomology). This implies that the …

PONTRYAGIN DUALITY FOR VARIETIES OVER p-ADIC FIELDS Page 1 J. Inst. Math. Jussieu
(2022), 1–38 doi:10.1017/S1474748022000469 © The Author(s), 2022. Published by …

Let $ X $ be a smooth projective variety over a finitely generated field $ K $ of characteristic~
$0 $ and fix an embedding $ K\subset\mathbb {C} $. The Mumford--Tate conjecture is a …

We give evidence for the refined version of the Beilinson–Bloch conjecture involving
coniveau filtrations, by studying several infinite families of CM motives (indexed by the …

One of the main results of this article is a proof of the rank-one case of an existence
conjecture on lisse Q¯ ℓ-sheaves on a smooth variety U over a finite field due to Deligne and …

Let k be an algebraically closed field of characteristic p> 0. Let be the ring of Witt vectors with
coefficients in k. We prove a motivic conjecture of Milne that relates, in the case of abelian …

Let K be a field of characteristic zero that is complete with respect to a discrete valuation,
with perfect residue field of characteristic p> 0. We formulate the notion of totally degenerate …

For a smooth proper variety over a p-adic field, its Brauer group and abelian fundamental
group are related to higher Chow groups by the Brauer–Manin pairing and class field theory …