#### Alladi Ramakrishnan Hall

#### Conductors and minimal discriminants of hyperelliptic curves

#### V. Padmavati

##### MIT

*The Ogg-Saito formula relates the Artin conductor of the minimal proper *

regular model of an elliptic curve over a local field (which is a

certain numerical invariant that can be computed from the Galois action

on étale cohomology groups) with the valuation of the discriminant of a

minimal Weierstrass equation for the curve. The definition of the Artin

conductor naturally extends to models of curves of higher genus as well.

Lower bounds on the Artin conductor of a regular model can be used to

give upper bounds on the number of components of the special fiber of

the model, and this has applications to the study of rational points

(Chabauty's method). We show that the Artin conductor for the minimal

proper regular model of a hyperelliptic curve with rational Weierstrass

points, over a local field with perfect residue field (and residue

characteristic either zero or large enough compared to the genus) is

bounded above by the valuation of the discriminant of an integral

Weierstrass equation for the curve.

Done