Cohomology of local systems on the moduli of principally polarized abelian surfaces
| Autor: | Dan Petersen |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Cusp (singularity)
Pure mathematics Conjecture Mathematics - Number Theory Mathematics::Number Theory General Mathematics 010102 general mathematics Galois module 01 natural sciences Cohomology Moduli Mathematics - Algebraic Geometry 0103 physical sciences FOS: Mathematics Sheaf Number Theory (math.NT) 010307 mathematical physics 0101 mathematics Abelian group Algebraic Geometry (math.AG) 11F46 14K10 11G18 11F67 11F75 Stack (mathematics) Mathematics |
| Zdroj: | Pacific Journal of Mathematics. 275:39-61 |
| ISSN: | 0030-8730 |
| DOI: | 10.2140/pjm.2015.275.39 |
| Popis: | Let A_2 be the moduli stack of principally polarized abelian surfaces and V a smooth l-adic sheaf on A_2 associated to an irreducible rational finite dimensional representation of Sp(4). We give an explicit expression for the cohomology of V in any degree in terms of Tate type classes and Galois representations attached to elliptic and Siegel cusp forms. This confirms a conjecture of Faber and van der Geer. As an application we prove a dimension formula for vector-valued Siegel cusp forms for Sp(4,Z) of weight three, which had been conjectured by Ibukiyama. Comment: 18 pages. v3: Added a proof of a dimension formula for vector-valued Siegel cusp forms for Sp(4,Z) of weight three, previously conjectured by Ibukiyama. v4: Many minor changes and improvements. Final version, to appear in Pacific Journal of Mathematics |
| Databáze: | OpenAIRE |
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