ON MIXED HODGE STRUCTURES OF SHIMURA VARIETIES ATTACHED TO INNER FORMS OF THE SYMPLECTIC GROUP OF DEGREE TWO

• ODA TAKAYUKI

  Graduate School of Mathematical Sciences, University of Tokyo

• SCHWERMER JOACHIM

  Faculty of Mathematics, University of Vienna

抄録

We study arithmetic varieties $V$ attached to certain inner forms of $\boldsymbol{Q}$-rank one of the split symplectic $\boldsymbol{Q}$-group of degree two. These naturally arise as unitary groups of a 2-dimensional non-degenerate Hermitian space over an indefinite rational quaternion division algebra. First, we analyze the canonical mixed Hodge structure on the cohomology of these quasi-projective varieties and determine the successive quotients of the corresponding weight filtration. Second, by interpreting the cohomology groups within the framework of the theory of automorphic forms, we determine the internal structure of the cohomology “at infinity” of $V$, that is, the part which is spanned by regular values of suitable Eisenstein series or residues of such. In conclusion, we discuss some relations between the mixed Hodge structure and the so called Eisenstein cohomology. For example, we show that the Eisenstein cohomology in degree two consists of algebraic cycles.

収録刊行物

• Ｔｏｈｏｋｕ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｊｏｕｒｎａｌ，　Ｓｅｃｏｎｄ　Ｓｅｒｉｅｓ

  Ｔｏｈｏｋｕ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｊｏｕｒｎａｌ，　Ｓｅｃｏｎｄ　Ｓｅｒｉｅｓ 61 (1), 83-113, 2009

  東北大学大学院理学研究科数学専攻

キーワード

• Cohomology of arithmetic groups
• automorphic forms

詳細情報

• CRID: 1390001205119249792
• NII論文ID: 110007031055
• NII書誌ID: AA00863953
• DOI: 10.2748/tmj/1238764548
• ISSN: 2186585X
• ISSN: 00408735
• MRID: 2501864
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可