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Theses

Pureté des fibres de Springer affines pour GL_4

Abstract : This thesis consists of two parts. In the first part, we prove the purity of affine Springer fibers for GL₄ in the unramified case. More precisely, we have constructed a family of non standard affine pavings for the affine grassmannian, which induce an affine paving for the affine Springer fiber. In the second part, we introduce a notion of ξ-stability on the affine grassmannian X for the group G=GL_{d}, and we calculate the Poincaré polynomial of the quotient X^{ξ}/T of the stable part X^{ξ} by the maximal torus T by a process analogue to the Harder-Narasimhan reduction.
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Zongbin Chen. Pureté des fibres de Springer affines pour GL_4. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112266⟩. ⟨tel-00656163⟩

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