Add the following Liquid snippet to a product template (Sections/product-template.liquid) to show tags on a Shopify product page. The tags will correctly link back to the current product collection with the tag filters applied.

product-tags-snippet.liquid

{% if product.tags %}
  {% if collection.handle %}
    {% assign collection_scope = collection.handle %}
  {% else %}
    {% assign collection_scope = 'all' %}
  {% endif %}
  <ul class="product-tags">
    <li>Tags: </li>
    {% for tag in product.tags %}
      {% capture url %}/collections/{{ collection_scope }}/{{ tag | handleize }}{% endcapture %}
      <li>{{ tag | link_to: url }}</li>
    {% endfor %}
  </ul>
  <style media="screen">
  ul.product-tags {
    list-style-type: none;
    margin: 0;
    padding: 0;
  }
  ul.product-tags li {
    display: inline-block;
    font-weight: bold;
    text-transform: uppercase;
    letter-spacing: 1px;
    font-size: 12px;
  }
  ul.product-tags li a {
    text-decoration: none;
  }
  </style>
{% endif %}

This was written specifically for the District theme however it should work for any Shopify theme.

thanks a lot jonathanmoore, i used it on the Simple theme and it works great, a little styling and its fine. As i am new to shopify liquid staff, i called a render command on the new liquid file i created from your code and added it on the bottom of the product template.
Cheers