Godeaux–Serre varieties and the étale index

2013 ◽  
Vol 11 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Benjamin Antieau ◽  
Ben Williams
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Function Fields ◽  
Projective Representation ◽  
High Dimensional ◽  
Index Problem ◽  
Completion Theorem

AbstractWe use Godeaux–Serre varieties of finite groups, projective representation theory, the twisted Atiyah–Segal completion theorem, and our previous work on the topological period-index problem to compute the étale index of Brauer classes α ∈ Brét(X) in some specific examples. In particular, these computations show that the étale index of α differs from the period of α in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Godeaux–Serre varieties in terms of projective representation theory.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

scholarly journals FINITE GROUPS AS GALOIS GROUPS OF FUNCTION FIELDS WITH INFINITE FIELD OF CONSTANTS

2010 ◽  
Vol 88 (3) ◽  
pp. 301-312
Author(s):  
C. ÁLVAREZ-GARCÍA ◽  
G. VILLA-SALVADOR
Keyword(s):  
Finite Groups ◽  
Function Field ◽  
Function Fields ◽  
Galois Groups ◽  
Infinite Field ◽  
Separable Extension ◽  
Separable Extensions

AbstractLetE/kbe a function field over an infinite field of constants. Assume thatE/k(x) is a separable extension of degree greater than one such that there exists a place of degree one ofk(x) ramified inE. LetK/kbe a function field. We prove that there exist infinitely many nonisomorphic separable extensionsL/Ksuch that [L:K]=[E:k(x)] andAutkL=AutKL≅Autk(x)E.

scholarly journals Realization of finite groups over function fields

1973 ◽  
Vol 24 (1) ◽  
pp. 154-158
Author(s):  
Moshe Jarden
Keyword(s):  
Finite Groups ◽  
Function Fields

Induced and Produced Modules

1955 ◽  
Vol 7 ◽  
pp. 490-508 ◽  
Author(s):  
D. G. Higman
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Induced Representation

We shall consider here two generalizations to rings of the concept of induced representation as it occurs in the representation theory of finite groups (6).If A is a ring, S a subring of A, we shall associate with each S-module M an induced pair (I(M), K) consisting of an A -modulo I(M) and an S-homomorphism K: M → I(M).

Weights for Covering Groups of Symmetric and Alternating Groups, р ≠ 2

1991 ◽  
Vol 43 (4) ◽  
pp. 792-813 ◽  
Author(s):  
G. O. Michler ◽  
J. B. Olsson
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Conjugacy Class ◽  
Finite Groups ◽  
Irreducible Character ◽  
Modular Representation ◽  
Modular Representation Theory ◽  
A Finite Group ◽  
Covering Groups ◽  
Fundamental Paper

In his fundamental paper [1] J. L. Alperin introduced the idea of a weight in modular representation theory of finite groups G. Let p be a prime. A p-subgroup R is called a radical subgroup of G if R = Op(NG(R)). An irreducible character φ of NG(R) is called a weight character if φ is trivial on R and belongs to a p-block of defect zero of NG(R)/R. The G-conjugacy class of the pair (R, φ) is a weight of G. Let b be the p-block of NG(R) containing φ, and let B be p-block of G. A weight (R, φ) is a B-weight for the block B of G if B = bG, which means that B and b correspond under the Brauer homomorphism. Alperin's conjecture on weights asserts that the number l*(B) of B-weights of a p-block B of a finite group G equals the number l(B) of modular characters of B.

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