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Yellow Pig
Yellow Pig
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According to Chapter 4 of Beilinson, Bernstein, and Deligne's "Faisceaux Pervers" (Asterisque 100, 1980) the inverse image $f^*$$Rf^*$ with respect to a finite morphism $f$ is leftright t-exact with respect to the perverse t-structure. Is there an example that shows that it is not necessarily t-exact? Is there a class of finite morphisms other than the etale morphisms where it is t-exact?

According to Chapter 4 of Beilinson, Bernstein, and Deligne's "Faisceaux Pervers" (Asterisque 100, 1980) the inverse image $f^*$ with respect to a finite morphism $f$ is left t-exact with respect to the perverse t-structure. Is there an example that shows that it is not necessarily t-exact? Is there a class of finite morphisms other than the etale morphisms where it is t-exact?

According to Chapter 4 of Beilinson, Bernstein, and Deligne's "Faisceaux Pervers" (Asterisque 100, 1980) the inverse image $Rf^*$ with respect to a finite morphism $f$ is right t-exact with respect to the perverse t-structure. Is there an example that shows that it is not necessarily t-exact? Is there a class of finite morphisms other than the etale morphisms where it is t-exact?

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Yellow Pig
Yellow Pig
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Example to show that the inverse image under a finite morphism is not t-exact with respect to the perverse t-structure

According to Chapter 4 of Beilinson, Bernstein, and Deligne's "Faisceaux Pervers" (Asterisque 100, 1980) the inverse image $f^*$ with respect to a finite morphism $f$ is left t-exact with respect to the perverse t-structure. Is there an example that shows that it is not necessarily t-exact? Is there a class of finite morphisms other than the etale morphisms where it is t-exact?