I've just defended my PhD in mathematics and started a postdoc. While working on an improvement of one of the results of my thesis, I realized that there are several minor mistakes and a big bug in a proof that invalids a minor result in the thesis (about 3-4 pages out of 110). Unfortunately neither I nor my advisor or referees figured it out the mistake. Though the result is minor, it is announced in the introduction and the manuscript is on-line on an ArXiv-like server, so that I could publish a new version but not cancel the one on-line.
What is the best thing to do? Upload an errata? Upload a "revised" version of the thesis? Publish a "revised version" of the thesis on my web-page?
Can this damage my future career, making me look not "reliable" as a researcher?
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