论文标题
代数的brauer组成的品种
The algebraic Brauer group of a pinched variety
论文作者
论文摘要
米歇尔·布里恩（Michel Brion）提供了引理。其他（次要）变化。提交版本。 令k为任何字段，让x'为投射和几何积分k-scheme，让y'为有限的闭合X'。如果f：y' - > y是有限的k-schemes和x之间示意性的主导形态，则是通过F通过faia fia faiva fia f通过f将x'沿y'夹住，我们描述了诱导的bbr_ {1} x- {1} x-> br_> br_> br_ {1} x'bra and x'x x'x x'的内核（在某些情况下，在某些情况下，cokernel）（在某些情况下）。 x'_solely_在y和y'的残基字段的brauer组以及br k中的x and x'的阿米特族子组中。作为应用程序，我们计算了一个射影和几何积分k理性曲线（具有任意奇异性）的Brauer组。我们还将Roquette和Lichtebaum的著名定理扩展到任何本地领域的一类奇异曲线。
Added lemma provided by Michel Brion. Other (minor) changes. Submitted version. Let k be any field, let X' be a projective and geometrically integral k-scheme and let Y' be a finite closed subscheme of X'. If f: Y'-> Y is a schematically dominant morphism between finite k-schemes and X is obtained by pinching X' along Y' via f, we describe the kernel (and, in certain cases, the cokernel) of the induced pullback map Br_{1}X -> Br_{1}X' between the corresponding algebraic (cohomological) Brauer groups of X and X'_solely_ in terms of the Brauer groups of the residue fields of Y and Y' and the Amitsur subgroups of X and X' in Br k. As an application, we compute the Brauer group of a projective and geometrically integral k-rational curve (with arbitrary singularities) over any field k. We also extend a well-known theorem of Roquette and Lichtenbaum to a class of singular curves over any local field.
