Do inverse images respect flabby sheaves? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T23:56:55Z http://mathoverflow.net/feeds/question/77622 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77622/do-inverse-images-respect-flabby-sheaves Do inverse images respect flabby sheaves? Mikhail Bondarko 2011-10-09T20:13:44Z 2011-10-09T20:49:19Z <p>Let $i:Y\to X$ be a closed embedding of varieties, and let $S$ be a flabby \'etale (or Nisnevich) sheaf of abelian groups on $X$. Is $i^*S$ flabby also? I am mostly interested in the case when $S=i_{x*}C$, where $C$ is a constant sheaf on a geometric (or Nisnevich) not necessarily closed (!!) point $x$ of $X$, $i_x:x\to X$ is the corresponding morphism. In this particular case the statement seems easy to prove; yet I wonder whether it follows from some general statement, and what are the 'standard' references for this. Are any additional restrictions needed here?</p> <p>Also, I wonder whether sheaves of the type $i^*i_{x*}$ were studied somewhere in the literature?</p>