Seminar of Algebra

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Slopes and periods of connections

Jean-Baptiste Teyssier (Freie Universität, Berlin)
Departamento de Álgebra
Tue, 28 apr 2015 12:00

For a smooth algebraic variety $X$ over $\mathbb{C}$, the periods of $X$ are certain complex numbers obtained by integration of differential forms on $X$ along topological cycles drawn on $X^{\text{an}}$. As shown by Grothendieck and Deligne, algebraic regular connections on $X$ give rise to periods, and when varying in families, periods satisfy a differential equation with regular singularities.

This talk is an introduction to the ideas and notions that revolve around these results. We will also explain a recent progress on what can be said for periods of general algebraic connections, introduced by Bloch-Esnault in dimension 1 and Hien in any dimension. No prerequisite on $\mathcal{D}$-modules is necessary for this talk.