

Globus Seminar
May 30, 2013 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)






Real differential forms and currents on padic analytic spaces
Antoine Ducros^{} ^{} Institut de Mathématiques de Jussieu, Paris

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Abstract:
I will present a joint work with Antoine ChambertLoir, in which we develop kind of a "harmonic analysis" formalism on Berkovich spaces. More precisely, we define:
 real differential forms of bidegree (p,q) on a Berkovich space X of dimension n;
 the integral of a (n,n) form (with compact support) on X;
 the boundary integral of a (n,n1) form.
We have Stokes and Green formulas in this context. We define currents by duality, and the PoincaréLelong formula holds.
We are also able to associate to a metrized line bundle (L,.) a curvature form c_1(L,.) (if . is not smooth, this is not a form in general, but a current). If (L,.) comes from a formal model, c_1(L,.)^n is shown to be a measure, which coincides with a measure previously defined by ChambertLoir in terms of intersection theory on the special fiber (in his work on padic equidistribution of points of small height).

