Name:
Geometric_non-vanishing.pdf
Size:
579.0Kb
Format:
PDF
Description:
Final Accepted Manuscript
Author
Ulmer, DouglasAffiliation
Department of Mathematics, University of ArizonaIssue Date
2004-09-02
Metadata
Show full item recordPublisher
Springer Science and Business Media LLCCitation
Ulmer, D. (2005). Geometric non-vanishing. Inventiones mathematicae, 159(1), 133-186.Journal
Inventiones mathematicaeRights
Copyright © Springer-Verlag 2004.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We consider L-functions attached to representations of the Galois group of the function field of a curve over a finite field. Under mild tameness hypotheses, we prove non-vanishing results for twists of these L-functions by characters of order prime to the characteristic of the ground field and more generally by certain representations with solvable image. We also allow local restrictions on the twisting representation at finitely many places. Our methods are geometric, and include the Riemann-Roch theorem, the cohomological interpretation of L-functions, and monodromy calculations of Katz. As an application, we prove a result which allows one to deduce the conjecture of Birch and Swinnerton-Dyer for non-isotrivial elliptic curves over function fields whose L-function vanishes to order at most 1 from a suitable Gross-Zagier formula.Note
12 month embargo; published: 02 September 2004ISSN
0020-9910EISSN
1432-1297Version
Final accepted manuscriptae974a485f413a2113503eed53cd6c53
10.1007/s00222-004-0386-z