Artin-Whaples approximations of bounded degree on algebraic varieties (30')
speaker: Vincenzo Mantova (Università di Pisa)abstract: (Joint work with U. Zannier) The classical Artin-Whaples approximation theorem asserts that given $n$ absolute values over a field \(K\), and \(n\) associated points in \(\mathbb{P}_1(K)\), there exists a point in \(\mathbb{P}_1(K)\) that approximates simultaneously, and with arbitrary precision, each of the given points with respect to the corresponding absolute values. The Chinese Reminder Theorem is an elementary and well-known form of this statement. If we replace \(\mathbb{P}_1\) with another algebraic variety, several analogous results are possible, at the price of expanding the field of definition of the approximating points. We will present a generalisation that has a particularly simple proof, and produces an explicit uniform bound for the degree of the approximating point.
timetable:
Thu 27 Sep, 15:45 - 16:15, Sala Conferenze Centro De Giorgi
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