Analogue of Weil representation for abelian schemes
| dc.creator | Polishchuk, Alexander | |
| dc.date | 1997-12-19 | |
| dc.date.accessioned | 2026-07-07T01:51:25Z | |
| dc.date.available | 2026-07-07T01:51:25Z | |
| dc.description | In this paper we construct a projective action of certain arithmetic group on the derived category of coherent sheaves on an abelian scheme $A$, which is analogous to Weil representation of the symplectic group. More precisely, the arithmetic group in question is a congruence subgroup in the group of "symplectic" automorphisms of $A\times\hat{A}$ where $\hat{A}$ is the dual abelian scheme. The "projectivity" of this action refers to shifts in the derived category and tensorings with line bundles pulled from the base. In particular, if $A$ is an abelian scheme over $S$ equipped with an ample line bundle $L$ of degree 1 then we construct an action of a central extension of $Sp_{2n}(\Bbb Z)$ by $\Bbb Z\times Pic(S)$ on the derived category of coherent sheaves on $A^n$ (the $n$-th fibered power of $A$ over $S$). We describe the corresponding central extension explicitly using the the canonical torsion line bundle on $S$ associated with $L$. As a main technical result we prove the existence of a representation of rank $d$ for a symmetric finite Heisenberg group scheme of odd order $d^2$. | |
| dc.description | 39 pages, AMSLatex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9712021 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9712021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/294 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Analogue of Weil representation for abelian schemes | |
| dc.type | text |