Complexity bound of absolute factoring of parametric polynomials.
Component clusters for acyclic quivers
The theory of Caldero-Chapoton algebras of Cerulli Irelli, Labardini-Fragoso and Schröer (2015) leads to a refinement of the notions of cluster variables and clusters, via so-called component clusters. We compare component clusters to classical clusters for the cluster algebra of an acyclic quiver. We propose a definition of mutation between component clusters and determine the mutation relations of component clusters for affine quivers. In the case of a wild quiver, we provide bounds for the size...
Component groups of abelian varieties and Grothendieck's duality conjecture
We investigate Grothendieck’s pairing on component groups of abelian varieties from the viewpoint of rigid uniformization theory. Under the assumption that the pairing is perfect, we show that the filtrations, as introduced by Lorenzini and in a more general way by Bosch and Xarles, are dual to each other. Furthermore, the methods yield some progress on the perfectness of the pairing itself, in particular, for abelian varieties with potentially multiplicative reduction.
Comportement des de Bass dans les extensions plates
Composition of binary quadratic forms over integral domains
Composition of quaternary quadratic forms
Composition-diamond lemma for modules
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
Computation of Bett Numbers of Monomial Ideals Associated with Stacked Polytopes.
Computations in weighted polynomial rings.
Computations with Frobenius powers.
Computations with Witt vectors of length
In this paper we describe how to perform computations with Witt vectors of length in an efficient way and give a formula that allows us to compute the third coordinate of the Greenberg transform of a polynomial directly. We apply these results to obtain information on the third coordinate of the -invariant of the canonical lifting as a function on the -invariant of the ordinary elliptic curve in characteristic .
Computing Gröbner fans of toric ideals.
Computing Hilbert-Kunz functions of 1-dimensional graded rings.
Computing limit linear series with infinitesimal methods
Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor.Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined the Hilbert function...
Computing -removed -orderings and -orderings of order
We develop a recursive method for computing the -removed -orderings and -orderings of order the characteristic sequences associated to these and limits associated to these sequences for subsets of a Dedekind domain This method is applied to compute these objects for and .
Computing versal deformations.
Comultiplication modules over a pullback of Dedekind domains
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication -modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.
Concerning Filtrations on Commutative Rings.
Condition d’Ischebeck-Auslander et condition de Serre
Conditions under which and are almost Q-rings
All rings considered in this paper are assumed to be commutative with identities. A ring is a -ring if every ideal of is a finite product of primary ideals. An almost -ring is a ring whose localization at every prime ideal is a -ring. In this paper, we first prove that the statements, is an almost -ring and is an almost -ring are equivalent for any ring . Then we prove that under the condition that every prime ideal of is an extension of a prime ideal of , the ring is a (an almost)...