A down to earth introduction to anabelian geometry
Abstract
Anabelian geometry is the study of a series of daring conjectures formulated by Grothendieck about the interactions between the geometric, topologic and arithmetic aspects of hyperbolic Riemann surfaces. Let g>=2 be an integer and write Pg for the profinite completion of the fundamental group of the compact, oriented surface of genus g. If X is a Riemann surface of genus g defined by an equation with coefficients in Q (more generally, a number field), then X induces an outer action of the absolute Galois group of Q on Pg. Loosely speaking, Grothedieck's anabelian conjectures aim to reconstruct X completely from this outer action. We are going to explain these conjectures together with some of the ideas and results which inspired Grothendieck. Finally, we will state some of the most important results available.
ll seminario si terrà in modalità mista.
Tutti gli interessati a partecipare in presenza devono contattare per email al Prof. Andrea Malchiodi (andrea.malchiodi@sns.it)
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