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We define and study new filtrations called of stratification of a perverse sheaf on a scheme; beside the cases of the weight or monodromy filtrations, these filtrations are available whatever are the ring of coefficients. We illustrate these constructions in the geometric situation of the simple unitary Shimura varieties of Harris and Taylors book for the perverse sheaves of Harris-Taylor and the complex of vanishing cycles, introduced and studied in my 2009 paper at inventiones. In the situation studied in loc. cit., we show how to use these filtrations to simplify the principal step of this paper; the cases of finite field or ring of integer of a local field will be studied in the next published paper.
We introduce a notion of positive pair of contact structures on a 3-manifold which generalizes a previous definition of Eliashberg-Thurston and Mitsumatsu. Such a pair gives rise to a locally integrable plane field $lambda$. We prove that if $lambda$
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces of Sobole
The legacy of Jordans canonical form on Poincares algebraic practices. This paper proposes a transversal overview on Henri Poincares early works (1878-1885). Our investigations start with a case study of a short note published by Poincare on 1884 : S
Let ${rm F}$ be a rank-2 semi-stable sheaf on the projective plane, with Chern classes $c_{1}=0,c_{2}=n$. The curve $beta_{rm F}$ of jumping lines of ${rm F}$, in the dual projective plane, has degree $n$. Let ${rm M}_{n}$ be the moduli space of equi
The effect of leverage on liquidity is a tool for analysing the level of liquidity for a given production process. It measures the sensitivity of the level of liquidity that results from changes in the volume of production and unit operating margin.