Arithmetic Algebraic Geometry of Curves

We will study the connections in between algebraic number theory and one-dimensional schemes (curves). More specifically we will cover: integral closures, plane curves, factorisation of ideals, the discriminants, the ideal class group, projective curves, nonsingular complete curves, zeta-functions and the Riemann-Roch Theorem. If time permits we will also cover Frobenius morphisms and the Riemann hypothesis and further topics like the Jacobian variety and Galois representations.

Pavel Stoilescu

Australian National University

Pavel is currently a third-year pure mathematics student at the Australian National University. He is particularly interested in geometry and algebra.

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