[iasmath-semru] Working group on lisse etale sheaves: first announcement

[Kiran S. Kedlaya]

Daniel Litt and I are planning to organize a working group next
semester centered on Deligne's Conjecture 1.2.10 from "La Conjecture de
Weil, II", which predicts various good behaviors of lisse etale sheaves.

Sample topics might include the following (but additional suggestions
are also welcome).

-- The formulation of the Langlands correspondence for GL(n) over a
function field (as proved by L. Lafforgue for etale cohomology and T.
Abe for p-adic cohomology), and what it says about coefficient objects
on curves.

-- The behavior of fundamental groups upon restriction to suitable
curves (Lefschetz principle), and its application to the theory of
weights on higher-dimensional varieties.

-- Deligne's argument for uniform algebraicity of Frobenius eigenvalues
(and the Esnault-Kerz treatment thereof).

-- Drinfeld's construction of compatible systems in etale cohomology.

-- Some background on p-adic Weil cohomology (rigid cohomology), and the
analogues of lisse Weil sheaves therein (convergent and overconvergent
F-isocrystals).

-- Newton polygons for l-adic and p-adic sheaves (including work of V.
Lafforgue, Drinfeld--Kedlaya, Kramer-Miller).

-- The role of Bertini-type theorems over finite fields (Poonen's
theorem and its generalizations) in the aforementioned results.

-- Applications of the Langlands correspondence to integrality of
monodromy of rigid local systems (Esnault-Groechenig).

-- De Jong's conjecture on deformation of mod-l Galois representations
(theorem of Gaitsgory).

If time permits, at the end of the term I may speak about the extension
of compatible systems to include p-adic cohomology (i.e., the
construction of the "petit camarade cristallin" of an l-adic sheaf).

If you are interested in participating, please let me know by emailing
kedlaya at ias.edu. I will fix a weekly meeting time once I have a sense of
who is planning to come and what schedule constraints exist (for
example, I plan to avoid Thursdays because they are too busy).

Kiran