In this work, we present a study on the fine-tuning of a pre-trained Large Language Model for abstractive summarization of long texts in Portuguese. To do so, we built a corpus gathering a collection of 7,450 public Health Sciences papers in Portuguese. We fine-tuned a pre-trained BERT model for Brazilian Portuguese (the BERTimbau) with this corpus. In a similar condition, we also trained a second model based on Long Short-Term Memory (LSTM) from scratch for comparison purposes. Our evaluation showed that the fine-tuned model achieved higher ROUGE scores, outperforming the LSTM based by 30 points for F1-score. The fine-tuning of the pre-trained model also stands out in a qualitative evaluation performed by assessors, to the point of generating the perception that the generated summaries could have been created by humans in a specific collection of documents in the Health Sciences domain.