Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Lefschetz Motives and the Tate Conjecture

  • J. S. MILNE
  • Journal:
    Compositio Mathematica / Volume 117 / Issue 1 / May 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 47-81
    Print publication:
    May 1999
    • Article
      • You have access
    • PDF
    • Export citation

  • A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define Q-linear Tannakian categories of abelian motives using the Lefschetz classes as correspondences, and we compute the fundamental groups of the categories. As an application, we prove that the Hodge conjecture for complex abelian varieties of CM-type implies the Tate conjecture for all Abelian varieties over finite fields, thereby reducing the latter to a problem in complex analysis.

  • Motives with Galois Group of type G$_2$: an Exceptional Theta-Correspondence

  • BENEDICT H. GROSS, GORDAN SAVIN
  • Journal:
    Compositio Mathematica / Volume 114 / Issue 2 / November 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 153-217
    Print publication:
    November 1998
    • Article
      • You have access
    • PDF
    • Export citation

  • In this paper, we study an exceptional theta correspondence, obtained by restricting the minimal automorphic representation of the adjoint group of type E$_7$ and rank 3 over Q to the dual pair GxPGSp$_6$. Here G is the anisotropic form of G$_2$ over Q; using the correspondence, we lift certain automorphic forms on G to holomorphic cusp forms on PGSp$_6$. This lifting provides the first step in a project to construct motives of rank 7 and weight O over Q with Galois group of type G$_2$.