Period sheaves via derived de Rham cohomology
نویسندگان
چکیده
In this article we give an interpretation, in terms of derived de Rham complexes, Scholze's period sheaf and Tan--Tong's crystalline sheaf.
منابع مشابه
Algebraic de Rham cohomology
Before we continue, we need to point out some properties of algebraic de Rham cohomology. In other words, we will first prove some of the axioms before introducing the trace map and cohomology classes. Note that the axioms of a Weil cohomology theory do not provide for the existence of cohomology groups defined for nonprojective varieties, but that we may use the fact that they are defined for ...
متن کاملCrystalline Cohomology and De Rham Cohomology
The goal of this short paper is to give a slightly different perspective on the comparison between crystalline cohomology and de Rham cohomology. Most notably, we reprove Berthelot’s comparison result without using pd-stratifications, linearisations, and pd-differential operators. Crystalline cohomology is a p-adic cohomology theory for varieties in characteristic p created by Berthelot [Ber74]...
متن کاملLecture 15. de Rham cohomology
(Here we really mean the integral over Σ of the form obtained by pulling back ω under the inclusion map). Now suppose we have two such submanifolds, Σ0 and Σ1, which are (smoothly) homotopic. That is, we have a smooth map F : Σ × [0, 1] → M with F |Σ×{i} an immersion describing Σi for i = 0, 1. Then d(F∗ω) is a (k + 1)-form on the (k + 1)-dimensional oriented manifold with boundary Σ × [0, 1], ...
متن کاملIntroduction to De Rham Cohomology
We briefly review differential forms on manifolds. We prove homotopy invariance of cohomology, the Poincaré lemma and exactness of the Mayer–Vietoris sequence. We then compute the cohomology of some simple examples. Finally, we prove Poincaré duality for orientable manifolds.
متن کاملOn Quantum De Rham Cohomology
We define quantum exterior product ∧h and quantum exterior differential dh on Poisson manifolds, of which symplectic manifolds are an important class of examples. Quantum de Rham cohomology is defined as the cohomology of dh. We also define quantum Dolbeault cohomology. Quantum hard Lefschetz theorem is proved. We also define a version of quantum integral, and prove the quantum Stokes theorem. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2021
ISSN: ['0010-437X', '1570-5846']
DOI: https://doi.org/10.1112/s0010437x21007545