1. CMB 2013 (vol 57 pp. 439)
 Yang, YanHong

The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus2 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 2013 (vol 57 pp. 449)
 Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim

ZLamenability 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
HodgeWitt. This is proved by generalizing to the case of
threefolds a wellknown criterion due to N.~Nygaard for surfaces to be HodgeWitt.
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, HodgeWitt, 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 
