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Number Theory Seminar
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2008/01/23
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Weizhe Zheng (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
Weizhe Zheng (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
[ Abstract ]
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
