Cohomology Operations and the Deligne Conjecture
نویسنده
چکیده
The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.
منابع مشابه
Academy of Sciences of the Czech Republic Mathematical Institute Cohomology Operators and the Deligne Conjecture
The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.
متن کاملD-bar Spark Theory and Deligne Cohomology
We study the Harvey-Lawson spark characters of level p on complex manifolds. Presenting Deligne cohomology classes by sparks of level p, we give an explicit analytic product formula for Deligne cohomology. We also define refined Chern classes in Deligne cohomology for holomorphic vector bundles over complex manifolds. Applications to algebraic cycles are given. A Bott-type vanishing theorem in ...
متن کاملCOHOMOLOGY OF DELIGNE-LUSZTIG VARIETIES FOR UNIPOTENT BLOCKS OF GLn(q)
We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of GLn(q). We show that the geometric version of Broué’s conjecture over Q , together with Craven’s formula, holds for any unipotent block whenever it holds for the principal Φ1-block.
متن کاملCohomology of Deligne–Lusztig Varieties, Broué’s Conjecture, and Brauer Trees
In this paper, we present a conjecture on the degree of unipotent characters in the cohomology of particular Deligne–Lusztig varieties for groups of Lie type, and derive consequences of it. These degrees are a crucial piece of data in the geometric version of Broué’s abelian defect group conjecture, and can be used to verify this geometric conjecture in new cases. The geometric version of Broué...
متن کاملHodge-type Conjecture for Higher Chow Groups
Let X be a smooth quasi-projective variety over the algebraic closure of the rational number field. We show that the cycle map of the higher Chow group to Deligne cohomology is injective and the higher Hodge cycles are generated by the image of the cycle map as conjectured by Beilinson and Jannsen, if the cycle map to Deligne cohomology is injective and the Hodge conjecture is true for certain ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008