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Cohomological descentFri, 2018-Mar-23 00:34 UTC Length - 2:07 Welcome to random Wiki of the Day where we read the summary of a random Wikipedia page every day. The random article for Friday, 23 March 2018 is Cohomological descent. In algebraic geometry, a cohomological descent is, roughly, a "derived" version of a fully faithful descent in the classical descent theory. This point is made precise by the below: the following are equivalent: in an appropriate setting, given a map a from a simplicial space X to a space S, a ∗ : D + ( S ) → D + ( X ) {\displaystyle a^{*}:D^{+}(S)\to D^{+}(X)} is fully faithful. The natural transformation id D + ( S ) → R a ∗ ∘ a ∗ {\displaystyle \operatorname {id} _{D^{+}(S)}\to Ra_{*}\circ a^{*}} is an isomorphism. The map a is then said to be a morphism of cohomological descent. The treatment in SGA uses a lot of topos theory. Conrad's notes gives a more down-to-earth exposition. This recording reflects the Wikipedia text as of 00:34 UTC on Friday, 23 March 2018. For the full current version of the article, go to http://en.wikipedia.org/wiki/Cohomological_descent. This podcast is produced by Abulsme Productions based on Wikipedia content and is released under a Creative Commons Attribution-ShareAlike License. Visit wikioftheday.com for our archives, sister podcasts, and swag. Please subscribe to never miss an episode. You can also follow @WotDpod on Twitter. Abulsme Productions produces the current events podcast Curmudgeon's Corner as well. Check it out in your podcast player of choice. This has been Aditi. Thank you for listening to random Wiki of the Day. |

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