标题： 忠实地呈现的态射和相干逆像 显示英文标题

标题： Tamely presented morphisms and coherent pullback

摘要： 我们研究了无限类型中的两类态射：温和可表态射和具有相干逆像的态射。这些分别是有限可表态射和有限Tor维数态射的推广。 温和可表概型和stacks的类足够受限，从而从凝聚层理论的角度保留了有限类型概型的关键特征，但又足够广泛以包含几何表示论中有兴趣的许多无限类型例子。 对角线具有相干逆像的条件是光滑性在温和可表情形下的自然推广，我们证明这类对象保留了光滑簇的许多良好上同调性质。 我们的结果受启发于双重仿射赫克范畴及其在库仑分支理论相关范畴中卷积乘积的研究。 显示英文摘要

摘要： We study two classes of morphisms in infinite type: tamely presented morphisms and morphisms with coherent pullback. These are generalizations of finitely presented morphisms and morphisms of finite Tor-dimension, respectively. The class of tamely presented schemes and stacks is restricted enough to retain the key features of finite-type schemes from the point of view of coherent sheaf theory, but wide enough to encompass many infinite-type examples of interest in geometric representation theory. The condition that a diagonal has coherent pullback is a natural generalization of smoothness to the tamely presented setting, and we show such objects retain many good cohomological properties of smooth varieties. Our results are motivated by the study of convolution products in the double affine Hecke category and related categories in the theory of Coulomb branches.