A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof
We consider arithmetic varieties endowed with an action of the group scheme of n-th roots of unity and we define equivariant arithmetic K 0-theory for these varieties. We use the equivariant analytic torsion to define direct image maps in this context and we prove a Riemann-Roch theorem for the natu...
| Hauptverfasser: | , |
|---|---|
| Format: | Journal article |
| Veröffentlicht: |
Springer Verlag
2001
|
| _version_ | 1826302944306266112 |
|---|---|
| author | Köhler, K Roessler, D |
| author_facet | Köhler, K Roessler, D |
| author_sort | Köhler, K |
| collection | OXFORD |
| description | We consider arithmetic varieties endowed with an action of the group scheme of n-th roots of unity and we define equivariant arithmetic K 0-theory for these varieties. We use the equivariant analytic torsion to define direct image maps in this context and we prove a Riemann-Roch theorem for the natural transformation of equivariant arithmetic K 0-theory induced by the restriction to the fixed point scheme; this theorem can be viewed as an analog, in the context of Arakelov geometry, of the regular case of the theorem proved by P. Baum, W. Fulton and G. Quart in [BaFQ]. We show that it implies an equivariant refinement of the arithmetic Riemann-Roch theorem, in a form conjectured by J.-M. Bismut (cf. [B2, Par. (l), p. 353] and also Ch. Soulé’s question in [SABK, 1.5, p. 162]). |
| first_indexed | 2024-03-07T05:55:08Z |
| format | Journal article |
| id | oxford-uuid:ea41d2e5-b39e-4108-a652-945ede10c7a0 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:55:08Z |
| publishDate | 2001 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:ea41d2e5-b39e-4108-a652-945ede10c7a02022-03-27T11:00:36ZA fixed point formula of Lefschetz type in Arakelov geometry I: statement and proofJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ea41d2e5-b39e-4108-a652-945ede10c7a0Symplectic Elements at OxfordSpringer Verlag2001Köhler, KRoessler, DWe consider arithmetic varieties endowed with an action of the group scheme of n-th roots of unity and we define equivariant arithmetic K 0-theory for these varieties. We use the equivariant analytic torsion to define direct image maps in this context and we prove a Riemann-Roch theorem for the natural transformation of equivariant arithmetic K 0-theory induced by the restriction to the fixed point scheme; this theorem can be viewed as an analog, in the context of Arakelov geometry, of the regular case of the theorem proved by P. Baum, W. Fulton and G. Quart in [BaFQ]. We show that it implies an equivariant refinement of the arithmetic Riemann-Roch theorem, in a form conjectured by J.-M. Bismut (cf. [B2, Par. (l), p. 353] and also Ch. Soulé’s question in [SABK, 1.5, p. 162]). |
| spellingShingle | Köhler, K Roessler, D A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof |
| title | A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof |
| title_full | A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof |
| title_fullStr | A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof |
| title_full_unstemmed | A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof |
| title_short | A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof |
| title_sort | fixed point formula of lefschetz type in arakelov geometry i statement and proof |
| work_keys_str_mv | AT kohlerk afixedpointformulaoflefschetztypeinarakelovgeometryistatementandproof AT roesslerd afixedpointformulaoflefschetztypeinarakelovgeometryistatementandproof AT kohlerk fixedpointformulaoflefschetztypeinarakelovgeometryistatementandproof AT roesslerd fixedpointformulaoflefschetztypeinarakelovgeometryistatementandproof |