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THE HODGE CONJECTURE AND ARITHMETIC QUOTIENTS OF COMPLEX BALLS
HODGE CONJECTURE ARITHMETIC QUOTIENTS COMPLEX BALLS
2015/10/14
Let S be a closed Shimura variety uniformized by the complex n-ball. The Hodge conjecture predicts that every Hodge class in H2k(S, Q), k = 0, . . . , n, is algebraic. We show that this holds for all ...
For any linear quotient of a sphere, X = Sn−1/Γ, where Γ is an elementary abelian p–group, there is a corresponding Fp representable matroid MX which only depends on the isometry class of X. Whe...
An Application of Harnack Inequalitise to Random Walk on Nilpotent Quotients
Applications nilpotent quotients random walk
2015/7/14
An Application of Harnack Inequalitise to Random Walk on Nilpotent Quotients。
On the graded quotients of the ring of Fricke characters of a free group
Ring of Fricke characters Automorphism groups of free groups Andreadakis-Johnson filtration
2012/6/27
First, we study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of a free group acts. Then using it, we define a descendin...
Arithmetic groups with isomorphic finite quotients
Arithmetic groups isomorphic finite quotients Group Theory
2011/9/16
Abstract: Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class of) an S-ar...
Symmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals
Symmetric chain decomposition Boolean algebras cyclic crystals
2011/9/15
Abstract: The quotient of a Boolean algebra by a cyclic group is proven to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime order,...
Bicyclic semigroups of left I-quotients
bicyclic semigroup bisimple inverse w-semigroup I-quotients Iorder
2011/9/13
Abstract: In this article we study left I-orders in the bicyclic monoid $\mathcal{B}$. We give necessary and sufficient conditions for a subsemigroup of $\mathcal{B}$ to be a left I-oreder in $\mathca...
Some Quotients of the Boolean Lattice are Symmetric Chain Orders
symmetric chain decomposition Boolean lattice
2011/8/26
Abstract: R. Canfield has conjectured that for all subgroups G of the automorphism group of the Boolean lattice B(n) (which can be regarded as the symmetric group S(n)) the quotient order B(n)/G is a ...
Points rationnels sur les quotients d'Atkin-Lehner de courbes de Shimura de discriminant $pq$
Points rationnels quotients d’Atkin-Lehner
2011/2/21
Let p and q be two distinct prime numbers, and Xpq/wq be the quotient of the Shimura curve of discriminant pq by the Atkin-Lehner involution wq. We describe a way to verify in wide generality a criter...
We compute presentations for the finite quotients $\mathcal{G}_n=\mathcal{G}/St_\mathcal{G}(n)$ of the Grigorchuk group $\mathcal{G}$. We show that Schur Multipliers of these quotients are $H_2(\math...
Limits of quotients of real analytic functions in two variables
quotients real analytic functions variables
2010/11/12
Necessary and sufficient conditions for the existence of limits of the form {equation*} \lim_{(x,y)\rightarrow (a,b)}\frac{f(x,y)}{g(x,y)} {equation*} are given, under the hipothesis that $f$ and $g$...
Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers
Boundary quotients Toeplitz algebra affine semigroup natural numbers
2010/12/8
We study the Toeplitz algebra T (N ⋊ N×) and three quotients of this algebra: the C-algebra QN recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative bound...
Simple closed curves, word length, and nilpotent quotients of free groups
ISimple closed curves word length nilpotent quotients of free groups
2010/11/29
We consider the fundamental group p of a surface of finite type equipped with the infinite generating set consisting of all simple closed curves. We show that every nilpotent quotient of p has finite ...
A note on $(\alpha, \beta)$-higher derivations and their extensions to modules of quotients
derivation higher derivation ring of quotients module of quotients
2010/12/3
We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of ( , )-derivation to ( , )-higher derivation and demonstrate that a filter of a...
Quotients by actions of the derived group of a maximal unipotent subgroup
Quotients derived group of a maximal unipotent subgroup
2010/12/9
The ground field k is algebraically closed and of characteristic zero. Let G be a semisimple
algebraic group with Lie algebra g. Fix a maximal unipotent subgroup U ⊂ G and a maximal torus T of ...