O'Reilly logo

The Riemann Hypothesis for Function Fields by Machiel van Frankenhuijsen

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

1

Valuations

Valuations correspond to orbits of points on a curve: every orbit of Frobenius gives a valuation, and every valuation gives an orbit. This will be elaborated in Chapter 5. In this chapter, we study how valuations distinguish constants from nonconstant functions and how valuations can ramify.

We first develop this theory for an arbitrary extension L/K. In Section 1.4, we apply our theory to the situation that is the subject of this book, where L/K is a finite extension K/q of the field of rational functions image over the finite field of constants

The embedding corresponds to the projection where a point on the curve projects to the ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required