We describe two conjectures, one strictly stronger than the
other, that give descriptions of the integral Bernstein center for
(that is, the center of the
category of smooth
-modules,
for a
-adic field and
an algebraically closed
field of characteristic
different from
)
in terms of Galois theory. Moreover, we show that the weak version of the conjecture
(for
),
together with the strong version of the conjecture for
, implies the strong
conjecture for
. In a
companion paper (Invent. Math. 214:2 (2018), 999–1022) we show that the strong conjecture for
implies the weak
conjecture for
;
thus the two papers together give an inductive proof of both conjectures.
The upshot is a description of the Bernstein center in purely Galois
theoretic terms; previous work of the author shows that this description
implies the conjectural “local Langlands correspondence in families” of
(Ann. Sci.Éc. Norm. Supér.47:4 (2014), 655–722).
PDF Access Denied
We have not been able to recognize your IP address
3.148.102.90
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
