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Fourier transform of $${\mathcal D}_{\chi,\mathbb{Q}}^ † (\infty)$$-modules. (Transformation de Fourier des $${\mathcal D}_{\chi,\mathbb{Q}}^ † (\infty)$$-modules.) (French) Zbl 0872.14011
Let $$\mathcal V$$ be a complete discrete valuation ring of unequal characteristics $$(0,p)$$, $$K$$ its fraction field and $$\mathcal X$$ the formal projective space over $$\mathcal V$$. In this note, the author studies the geometric Fourier transform $${\mathcal F}({\mathcal M})$$ of a bounded coherent complex $$\mathcal M$$ of $${\mathcal D}^\dagger_{{\mathcal X},\mathbf Q}(\infty)$$-modules. She shows that $${\mathcal F}({\mathcal M})$$ coincides with the naive Fourier transform coming from the automorphism $$F$$ of the weak completion $$A_N(K)^\dagger$$ of the Weyl algebra given by $$F(\partial_{x_i})=\pi x_i, F(x_i) = -\partial_{x_i}/\pi$$, where $$\pi^{p-1} = -p$$.
See also the reviewer’s remark in the preceding review [C. Huyghe, C. R. Acad. Sci., Paris, Sér. I 321, No. 5, 587-590 (1995)].

##### MSC:
 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials