## 代数学コロキウム

開催情報 水曜日　17:00～18:00　数理科学研究科棟(駒場) 056号室 今井 直毅, 三枝 洋一

### 2021年06月30日(水)

17:00-18:00   オンライン開催

Prismatic and q-crystalline sites of higher level (Japanese)
[ 講演概要 ]
Two new p-adic cohomology theories, called prismatic cohomology and q-crystalline cohomology, were defined for generalizing crystalline cohomology and they recover most known integral p-adic cohomology theories. On the other hand, higher level crystalline cohomology was defined for constructing p-adic cohomology theory over a ramified base. In this talk, for a positive integer m, we will give a construction of the level m primastic and q-crystalline sites and prove a certain equivalence between the category of crystals on the m-prismatic site or the m-q-crystalline site and that on the usual prismatic site or the usual q-crystalline site, which can be regarded as the prismatic analogue of the Frobenius descent. We will also prove the equivalence between the category of crystals on the m-prismatic site and that on the (m-1)-q-crystalline site.