History of tag 0ARD
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changed the proof
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2021-07-14 |
2a0ab40 |
Left adjoint inclusion derived complete modules
This was requested by Arthur Ogus
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assigned tag 0ARD
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2014-10-03 |
9a68c95
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Tags: Added new tags
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created statement with label lemma-derived-complete-modules in examples.tex
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2014-09-22 |
16ad184 |
Derived complete modules
Example due to Bhargav Bhatt
Here's one attempted example showing that filtered colimits are not
left exact. It's too simple, so I'm afraid I missed something!
Consider R = Z with I = (p). One has inclusions f_n:Z/p -----> Z/p^n
of I-complete R-modules given by multiplication by p^n. There is a
natural map from f_n to f_{n+1} given by the identity on the first
factor, and 'p' on the second. Now take the filtered colimit of these
inclusions in I-complete R-modules to get Z/p -----> 0 (as the derived
completion of Q_p/Z_p, as a complex, is Z_p[1]), which is not an
inclusion in this category.
Best wishes,
Bhargav
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