论文标题
Adelic Etric品种和Adelic Loop组
Adelic toric varieties and adelic loop groups
论文作者
论文摘要
我们研究了促进空间，该空间是正常的圆环品种上所有有限分支覆盖物的逆极限，分支将代数圆环作用下的不变分裂设置为不变的除数。这些是Adelic Abelian代数组的完成（压缩），这是代数圆环的详细完成。我们证明，图意的曲线化的矢量束类别类别是有限的感谢您品种的直接限制，涵盖了定义完成的有限福利。在复杂的投影线的情况下，我们获得了Adelic射击线P。我们在P上定义了全体形态矢量束。我们描述了它们的特性，并证明了伯克霍夫对这些群体的分解。我们证明，全体形态线束的阿德利奇·皮卡德（Adelic Picard）组是对理由的同构，并证明了Birkhoff-Grothendieck分裂定理，用于较高等级的较高等级。
We study the proalgebraic space which is the inverse limit of all finite branched covers over a normal toric variety with branching set the invariant divisor under the algebraic torus action. These are completions (compactifications) of the adelic abelian algebraic group which is the profinite completion of the algebraic torus. We prove that the vector bundle category of the proalgebraic toric completion of a toric variety is the direct limit of the respective categories of the finite toric varieties coverings defining the completion. In the case of the complex projective line we obtain as proalgebraic completion the adelic projective line P. We define holomorphic vector bundles over P. We also introduce the smooth, Sobolev and Wiener adelic loop groups and the corresponding Grassmannans; we describe their properties and prove Birkhoff's factorization for these groups. We prove that the adelic Picard group of holomorphic line bundles is isomorphic to the rationals and prove the Birkhoff-Grothendieck splitting theorem for holomorphic bundles of higher rank over P.
