diff --git a/book/src/design/implementation/fields.md b/book/src/design/implementation/fields.md
index 0a36bd9..bdee072 100644
--- a/book/src/design/implementation/fields.md
+++ b/book/src/design/implementation/fields.md
@@ -2,21 +2,23 @@
 
 The [Pasta curves](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/)
 are designed to be highly 2-adic, meaning that a large $2^S$
-[multiplicative subgroup](../../background/fields.md#multiplicative-subgroups) exists in
-each field. That is, we can write $p - 1 \equiv 2^S \cdot T$ with $T$ odd. For both Pallas
-and Vesta, $S = 32$; this helps to simplify the field implementations.
+[multiplicative subgroup](https://zcash.github.io/halo2/background/fields.html#multiplicative-subgroups)
+exists in each field. That is, we can write $p - 1 \equiv 2^S \cdot T$ with $T$ odd. For
+both Pallas and Vesta, $S = 32$; this helps to simplify the field implementations.
 
 ## Sarkar square-root algorithm (table-based variant)
 
 We use a technique from [Sarkar2020](https://eprint.iacr.org/2020/1407.pdf) to compute
-[square roots](../../background/fields.md#square-roots) in `pasta_curves`. The intuition
+[square roots](https://zcash.github.io/halo2/background/fields.html#square-roots) in
+`pasta_curves`. The intuition
 behind the algorithm is that we can split the task into computing square roots in each
 multiplicative subgroup.
 
 Suppose we want to find the square root of $u$ modulo one of the Pasta primes $p$, where
 $u$ is a non-zero square in $\mathbb{Z}_p^\times$. We define a $2^S$
-[root of unity](../../background/fields.md#roots-of-unity) $g = z^T$ where $z$ is a
-non-square in $\mathbb{Z}_p^\times$, and precompute the following tables:
+[root of unity](https://zcash.github.io/halo2/background/fields.html#roots-of-unity)
+$g = z^T$ where $z$ is a non-square in $\mathbb{Z}_p^\times$, and precompute the following
+tables:
 
 $$
 gtab = \begin{bmatrix}