Consider a complex Stein manifold and a subanalytic relatively compact Stein open subset of . We prove the vanishing on of the holomorphic temperate cohomology.
[Dem09] Complex analytic and differential geometry, 2009 (Open Content Book, https://www.math.uh.edu/~shanyuji/Complex/agbook.pdf)
[GR65] Analytic functions of several complex variables, Prentice Hall Series in Modern Analysis, Prentice Hall, 1965 | Zbl
[GS16] Construction of sheaves on the subanalytic site, Subanalytic sheaves and Sobolev spaces (Astérisque), Volume 383, Société Mathématique de France, 2016, pp. 1-60 | Zbl
[Pet17] Tempered subanalytic topology on algebraic varieties (2017) (https://arxiv.org/abs/1703.00870)
[Siu69] Noetherianness of rings of holomorphic functions on Stein compact subsets, Proc. Am. Math. Soc., Volume 21 (1969), pp. 483-489 | Zbl
[Sko21] A Dolbeault lemma for temperate currents, Ann. Henri Lebesgue, Volume 4 (2021), pp. 879-896 | DOI