Cup Products in Sheaf Cohomology

1986 ◽  
Vol 29 (4) ◽  
pp. 469-477 ◽  
Author(s):  
J. F. Jardine
Keyword(s):  
Hopf Algebra ◽  
Prime Number ◽  
Algebraic Groups ◽  
Closed Field ◽  
Algebra Structure ◽  
Sheaf Cohomology ◽  
Algebraically Closed Field ◽  
Cup Product ◽  
Hopf Algebra Structure ◽  
Cup Products

AbstractLet k be an algebraically closed field, and let l be a prime number not equal to char(k). Let X be a locally fibrant simplicial sheaf on the big étale site for k, and let Y be a k scheme which is cohomologically proper. Then there is a Künneth-type isomorphismwhich is induced by an external cup-product pairing. Reductive algebraic groups G over k are cohomologically proper, by a result of Friedlander and Parshall. The resulting Hopf algebra structure on may be used together with the Lang isomorphism to give a new proof of the theorem of Friedlander-Mislin which avoids characteristic 0 theory. A vanishing criterion is established for the Friedlander-Quillen conjecture.

scholarly journals Semisimple Hopf Algebras of Dimension 2q3

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Jingcheng Dong ◽  
Li Dai
Keyword(s):  
Hopf Algebra ◽  
Prime Number ◽  
Hopf Algebras ◽  
Closed Field ◽  
Semisimple Hopf Algebra ◽  
Algebraically Closed Field

AbstractLet q be a prime number, k an algebraically closed field of characteristic 0, and H a non-trivial semisimple Hopf algebra of dimension 2q

Some Results in the Connective K-Theory of Lie Groups

1988 ◽  
Vol 31 (2) ◽  
pp. 194-199
Author(s):  
L. Magalhães
Keyword(s):  
Hopf Algebra ◽  
Lie Groups ◽  
Lie Group ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
K Theory ◽  
Torsion Free ◽  
Connected Lie Group

AbstractIn this paper we give a description of:(1) the Hopf algebra structure of k*(G; L) when G is a compact, connected Lie group and L is a ring of type Q(P) so that H*(G; L) is torsion free;(2) the algebra structure of k*(G2; L) for L = Z2 or Z.

Classes of unipotent elements in simple algebraic groups. I

1976 ◽  
Vol 79 (3) ◽  
pp. 401-425 ◽  
Author(s):  
P. Bala ◽  
R. W. Carter
Keyword(s):  
Algebraic Group ◽  
Lie Algebra ◽  
Algebraic Groups ◽  
Adjoint Action ◽  
Conjugacy Classes ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Nilpotent Elements

LetGbe a simple adjoint algebraic group over an algebraically closed fieldK. We are concerned to describe the conjugacy classes of unipotent elements ofG. Goperates on its Lie algebra g by means of the adjoint action and we may consider classes of nilpotent elements of g under this action. It has been shown by Springer (11) that there is a bijection between the unipotent elements ofGand the nilpotent elements ofgwhich preserves theG-action, provided that the characteristic ofKis either 0 or a ‘good prime’ forG. Thus we may concentrate on the problem of classifying the nilpotent elements of g under the adjointG-action.

scholarly journals ON THE COALGEBRAIC RING AND BOUSFIELD–KAN SPECTRAL SEQUENCE FOR A LANDWEBER EXACT SPECTRUM

2004 ◽  
Vol 47 (3) ◽  
pp. 513-532 ◽  
Author(s):  
Martin Bendersky ◽  
John R. Hunton
Keyword(s):  
Hopf Algebra ◽  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Subject Classification ◽  
Homotopy Groups ◽  
Algebra Structure ◽  
Simple Description ◽  
Ring Spectrum ◽  
Hopf Algebra Structure

AbstractWe construct a Bousfield–Kan (unstable Adams) spectral sequence based on an arbitrary (and not necessarily connective) ring spectrum $E$ with unit and which is related to the homotopy groups of a certain unstable $E$ completion $X_E^{\wedge}$ of a space $X$. For $E$ an $\mathbb{S}$-algebra this completion agrees with that of the first author and Thompson. We also establish in detail the Hopf algebra structure of the unstable cooperations (the coalgebraic module) $E_*(\underline{E}_*)$ for an arbitrary Landweber exact spectrum $E$, extending work of the second author with Hopkins and with Turner and giving basis-free descriptions of the modules of primitives and indecomposables. Taken together, these results enable us to give a simple description of the $E_2$-page of the $E$-theory Bousfield–Kan spectral sequence when $E$ is any Landweber exact ring spectrum with unit. This extends work of the first author and others and gives a tractable unstable Adams spectral sequence based on a $v_n$-periodic theory for all $n$.AMS 2000 Mathematics subject classification: Primary 55P60; 55Q51; 55S25; 55T15. Secondary 55P47

Sign in / Sign up

Export Citation Format

Share Document