Computational Algebra Seminar: Bauch -- Montes Algorithm In Function Fields

Speaker: Jens Bauch
Title: Montes Algorithm In Function Fields
Time & Place: 4-5pm Thursday 26 April, Carslaw 535

Abstract:
Let $A=k[t]$ be the polynomial ring over the perfect field $k$ and 
$f\in A[x]$ be a monic irreducible separable polynomial. Denote by $F/k$ the
function field determined by $f$ and consider a given non-zero prime
ideal $\mathfrak{p}$ of $A$. The Montes algorithm determines a new
representation, so called OM-representation, of the prime ideals of the
(finite) maximal order of $F$ lying over $\mathfrak{p}$. This yields a
new representation of places of function fields. In this talk we
summarize briefly some applications of this new representation; that are
the computation of the genus, the computation of the maximal order, and
the improvement of the computation of Riemann-Roch spaces.