In this talk, we introduce the analytic de Rham stack for rigid
varieties over Qp
(and more general analytic stacks). This object is an
analytic incarnation of the (algebraic) de Rham stack of Simpson,
and encodes a theory of analytic D-modules...
I will discuss the following conjecture: an irreducible Q¯
ℓ-local system L on a smooth complex algebraic variety S arises in
cohomology of a family of varieties over S if and only if L can be
extended to an etale local system over some descent of S...
Multiplier ideals in characteristic zero and test ideals in
positive characteristic are fundamental objects in the study of
commutative algebra and birational geometry in equal
characteristic. We introduced a mixed characteristic version
of the...
With every bounded prism Bhatt and Scholze associated a
cohomology theory of formal p-adic schemes. The prismatic
cohomology comes equipped with the Nygaard filtration and the
Frobenius endomorphism. The Bhatt-Scholze construction has been
advanced...
