2,830 research outputs found
The Langlands-Kottwitz approach for some simple Shimura Varieties
We show how the Langlands-Kottwitz method can be used to determine the
semisimple local factors of the Hasse-Weil zeta-function of certain Shimura
varieties. On the way, we prove a conjecture of Haines and Kottwitz in this
special case.Comment: 23 page
Perfectoid spaces
We introduce a certain class of so-called perfectoid rings and spaces, which
give a natural framework for Faltings' almost purity theorem, and for which
there is a natural tilting operation which exchanges characteristic 0 and
characteristic p. We deduce the weight-monodromy conjecture in certain cases by
reduction to equal characteristic.Comment: 51 pages, 2 figure
The Langlands-Kottwitz approach for the modular curve
We show how the Langlands-Kottwitz method can be used to determine the local
factors of the Hasse-Weil zeta-function of the modular curve at places of bad
reduction. On the way, we prove a conjecture of Haines and Kottwitz in this
special case.Comment: 39 page
Prisms and Prismatic Cohomology
We introduce the notion of a prism, which may be regarded as a "deperfection"
of the notion of a perfectoid ring. Using prisms, we attach a ringed site ---
the prismatic site --- to a -adic formal scheme. The resulting cohomology
theory specializes to (and often refines) most known integral -adic
cohomology theories.
As applications, we prove an improved version of the almost purity theorem
allowing ramification along arbitrary closed subsets (without using adic
spaces), give a co-ordinate free description of -de Rham cohomology as
conjectured by the second author, and settle a vanishing conjecture for the
-adic Tate twists introduced in previous joint work with
Morrow.Comment: v2: minor update
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