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Calculations about multiplicities.

Manuel Abellanas (1982)

Revista Matemática Hispanoamericana

One gives a formula for the calculation of the local intersection multiplicity index of analytic varieties, analogous to the Bézout formula in the case of algebraic varieties in the projective space, in the case of normal crossings. One obtains also a recurrent process for the calculation of the local intersection multiplicity index of plane analytic curves.

Champs de vecteurs et formes différentielles sur une variété des points proches

Basile Guy Richard Bossoto, Eugène Okassa (2008)

Archivum Mathematicum

Let M be a smooth manifold, A a local algebra in sense of André Weil, M A the manifold of near points on M of kind A and 𝔛 ( M A ) the module of vector fields on M A . We give a new definition of vector fields on M A and we show that 𝔛 ( M A ) is a Lie algebra over A . We study the cohomology of A -differential forms. Résumé. On considère M une variété différentielle, A une algèbre locale au sens d’André Weil, M A la variété des points proches de M d’espèce A et 𝔛 ( M A ) le module des champs de vecteurs sur M A . On donne une nouvelle...

Cohen-Lenstra sums over local rings

Christian Wittmann (2004)

Journal de Théorie des Nombres de Bordeaux

We study series of the form M | Aut R ( M ) | - 1 | M | - u , where R is a commutative local ring, u is a non-negative integer, and the summation extends over all finite R -modules M , up to isomorphism. This problem is motivated by Cohen-Lenstra heuristics on class groups of number fields, where sums of this kind occur. If R has additional properties, we will relate the above sum to a limit of zeta functions of the free modules R n , where these zeta functions count R -submodules of finite index in R n . In particular we will show that...

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