Canadian Mathematical Society
Canadian Mathematical Society
  location:  Publicationsjournals
Search results

Search: All articles in the CMB digital archive with keyword Frobenius

  Expand all        Collapse all Results 1 - 4 of 4

1. CMB 2013 (vol 57 pp. 439)

Yang, YanHong
The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus-2 Curves $X$ in Charateristic $2$
We prove that for every ordinary genus-$2$ curve $X$ over a finite field $\kappa$ of characteristic $2$ with $\textrm{Aut}(X/\kappa)=\mathbb{Z}/2\mathbb{Z} \times S_3$, there exist $\textrm{SL}(2,\kappa[\![s]\!])$-representations of $\pi_1(X)$ such that the image of $\pi_1(\overline{X})$ is infinite. This result produces a family of examples similar to Laszlo's counterexample to de Jong's question regarding the finiteness of the geometric monodromy of representations of the fundamental group.

Keywords:vector bundle, Frobenius pullback, representation, etale fundamental group
Categories:14H60, 14D05, 14G15

2. CMB Online first

Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim
ZL-amenability Constants of Finite Groups with Two Character Degrees
We calculate the exact amenability constant of the centre of $\ell^1(G)$ when $G$ is one of the following classes of finite group: dihedral; extraspecial; or Frobenius with abelian complement and kernel. This is done using a formula which applies to all finite groups with two character degrees. In passing, we answer in the negative a question raised in work of the third author with Azimifard and Spronk (J. Funct. Anal. 2009).

Keywords:center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups
Categories:43A20, 20C15

3. CMB 2007 (vol 50 pp. 567)

Joshi, Kirti
Exotic Torsion, Frobenius Splitting and the Slope Spectral Sequence
In this paper we show that any Frobenius split, smooth, projective threefold over a perfect field of characteristic $p>0$ is Hodge--Witt. This is proved by generalizing to the case of threefolds a well-known criterion due to N.~Nygaard for surfaces to be Hodge-Witt. We also show that the second crystalline cohomology of any smooth, projective Frobenius split variety does not have any exotic torsion. In the last two sections we include some applications.

Keywords:threefolds, Frobenius splitting, Hodge--Witt, crystalline cohomology, slope spectral sequence, exotic torsion
Categories:14F30, 14J30

4. CMB 2007 (vol 50 pp. 447)

Śniatycki, Jędrzej
Generalizations of Frobenius' Theorem on Manifolds and Subcartesian Spaces
Let $\mathcal{F}$ be a family of vector fields on a manifold or a subcartesian space spanning a distribution $D$. We prove that an orbit $O$ of $\mathcal{F}$ is an integral manifold of $D$ if $D$ is involutive on $O$ and it has constant rank on $O$. This result implies Frobenius' theorem, and its various generalizations, on manifolds as well as on subcartesian spaces.

Keywords:differential spaces, generalized distributions, orbits, Frobenius' theorem, Sussmann's theorem
Categories:58A30, 58A40

© Canadian Mathematical Society, 2014 :