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Biomedical entity linking aims to map biomedical mentions, such as diseases and drugs, to standard entities in a given knowledge base. The specific challenge in this context is that the same biomedical entity can have a wide range of names, including synonyms, morphological variations, and names with different word orderings. Recently, BERT-based methods have advanced the state-of-the-art by allowing for rich representations of word sequences. However, they often have hundreds of millions of parameters and require heavy computing resources, which limits their applications in resource-limited scenarios. Here, we propose a lightweight neural method for biomedical entity linking, which needs just a fraction of the parameters of a BERT model and much less computing resources. Our method uses a simple alignment layer with attention mechanisms to capture the variations between mention and entity names. Yet, we show that our model is competitive with previous work on standard evaluation benchmarks.