Abrupt and unexpected terminations of software are termed as software crashes. They can be challenging to analyze. Finding the root cause requires extensive manual effort and expertise to connect information sources like stack traces, source code, and logs. Typical approaches to fault localization require either test failures or source code. Crashes occurring in production environments, such as that of SAP HANA, provide solely crash logs and stack traces. We present a novel approach to localize faults based only on the stack trace information and no additional runtime information, by fine-tuning large language models (LLMs). We address complex cases where the root cause of a crash differs from the technical cause, and is not located in the innermost frame of the stack trace. As the number of historic crashes is insufficient to fine-tune LLMs, we augment our dataset by leveraging code mutators to inject synthetic crashes into the code base. By fine-tuning on 64,369 crashes resulting from 4.1 million mutations of the HANA code base, we can correctly predict the root cause location of a crash with an accuracy of 66.9\% while baselines only achieve 12.6% and 10.6%. We substantiate the generalizability of our approach by evaluating on two additional open-source databases, SQLite and DuckDB, achieving accuracies of 63% and 74%, respectively. Across all our experiments, fine-tuning consistently outperformed prompting non-finetuned LLMs for localizing faults in our datasets.