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Zeta functions and L-series in positive characteristic

Linear and algebraic independence of P-adic Carlitz logarithms

speaker: Vincent Bosser (University of Caen)

abstract: Let \(k = \mathbb{F}_q(\theta)\), let \(P\in\mathbb{F}_q[\theta]\) be an irreducible polynomial, and let \(log(\alpha_1), \ldots , log(\alpha_n)\) be \(k\)-linearly independent \(P\)-adic Carlitz logarithms of elements in \(k\). We will explain how to prove that \(log(\alpha_1), \ldots , log(\alpha_n)\) are linearly independent over \(k\) and discuss the problems that arise when trying to prove that these numbers are algebraically independent. These questions are connected with Leopoldt conjecture for finite extensions of \(k\).

timetable:
Wed 28 Nov, 9:00 - 10:15, Sala Conferenze Centro De Giorgi
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