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Bases for Projective modules in An(k)
(2003-12)
Let $A_n(k)$ be the Weyl algebra, with $k$ a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let $M$ be a left submodule of a free module. ...
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Commensurability in Artin groups of spherical type
(EMS Press, 2021-06-29)
We give an almost complete classification of Artin groups of spherical type up to commensurability. Let A and A0 be two Artin groups of spherical type, and let A1; : : : ; Ap (respectively, A0 1; : : : ; A0 q) be the ...
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Los números de (Euler)-Catalan
(Asociación Matemática Venezolana, 2003)
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Fast Nielsen-Thurston classification of braids
(Mathematical Sciences Publishers, 2014)
We prove the existence of an algorithm that solves the reducibility problem in braid groups and runs in quadratic time with respect to the braid length for any fixed braid index.
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An Effective Criterion for Finite Monodromy of ℓ-Adic Sheaves
(Springer, 2023-02-01)
We provide an effective version of Katz’ criterion for finiteness of the monodromy group of a lisse, pure of weight zero, -adic sheaf on a normal variety over a finite field, depending on the numerical complexity of the sheaf.
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The characteristic cohomology class of a triangulated category
(2005)
The concept of a triangulated homotopy category can be canonically lifted to the level of a groupoid-enriched category. This way two natural axioms on track triangles replace the four somewhat obscure axioms of a triangulated ...
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Valuations in algebraic field extensions
(Elsevier, 2007-06-15)
Let K → L be an algebraic field extension and ν a valuation of K. The purpose of this paper is to describe the totality of extensions {ν′} of ν to L using a refined version of MacLane’s key polynomials. In the basic case ...
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On dilatation factors of braids on three strands
(World Scientific Publishing, 2015-04)
In this work we present a natural surjective map from rigid braids in B3 (in Garside sense) to SL2(N). This map provides an upper and a lower bound for the dilatation factor of a pseudo-Anosov 3-strand braid. These bounds ...
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On a determinantal formula of Tadić
(Johns Hopkins University Press, 2014-02)
We study a special class of irreducible representations of GLn over a local non-Archimedean field which we call ladder representations. This is a natural class in the admissible dual which contains the Speh representations. ...
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Algebraic computation of some intersection D-modules
(Springer, 2006)
Let X be a complex analytic manifold, D ⊂ X a locally quasi-homogeneous free divisor, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on X − D. In this ...