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Dear Elisenda,
I have been studying your very interesting thesis. Can you prove in some cases that your higher arithmetic Chow groups are compact, or does such a result seem very hard to prove? Do you have any ideas on how one would prove such a statement? I was told by Soule that if they were compact, their volume should be related to special values of zeta functions. However, I myself cannot at the moment imagine how one would actually prove any compactness result, except in the case of the Borel regulator of a number field.
I am very grateful for any response you may have on this, even if it is just that you do not have any results at the moment.
Kind regards,
Dear Andreas,
Thanks a lot for showing interest on my work, and sorry for this late response. I have had some personal issues lately that kept me busy!
I have thought about your question, but to be honest I am not familiar at all with these topics. I talked to my advisor, Burgos, and he doesn’t know either what the answer could be. However, not like in my case, he has worked in fields related to the Borel regulator and the special values of zeta functions. He offered to further discuss with you the issue, so you might consider emailing him with related questions.
I am not working on the field of arithmetic geometry right now, since I am trying to find my way into biology. I am totally open to help you with any doubts arisen from my thesis, but I am afraid to confess that my view about future work is quite limited.
I wish you luck with your thesis.
Kind regards,
Elisenda
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