It sounds possible. Archive pages have a built in query they execute if you want to filter you can create a template for just that category such as archive-{category}.php or if your going to filter more information like described you should use.
add_action( 'pre_get_posts', 'my_change_sort_order');
function my_change_sort_order($query){
if(is_archive()):
//Set the order ASC or DESC
$query->set( 'order', 'ASC' );
endif;
};
as you loop you can modify the output.
if (have_posts()) : while ( have_posts() ) : the_post(); ?>
<?php if($wp_query->current_post == 0): ?>
//current_post is the index of the post within the loop
// this will be your first post
<?php echo $post->title ?>
<?php echo get_field('publication_abstract'); ?>
<?php endif ?>
//this will be all other posts
//just the title no excerpt
<?php echo $post->title; ?>
<?php endwhile ?>