تقرير
Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory
| العنوان: | Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory |
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| المؤلفون: | Anderson, Dave, Gonzales, Richard, Payne, Sam |
| المصدر: | Alg. Number Th. 15 (2021) 341-385 |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry |
| الوصف: | We produce a Grothendieck transformation from bivariant operational $K$-theory to Chow, with a Riemann-Roch formula that generalizes classical Grothendieck-Verdier-Riemann-Roch. We also produce Grothendieck transformations and Riemann-Roch formulas that generalize the classical Adams-Riemann-Roch and equivariant localization theorems. As applications, we exhibit a projective toric variety $X$ whose equivariant $K$-theory of vector bundles does not surject onto its ordinary $K$-theory, and describe the operational $K$-theory of spherical varieties in terms of fixed-point data. In an appendix, Vezzosi studies operational $K$-theory of derived schemes and constructs a Grothendieck transformation from bivariant algebraic $K$-theory of relatively perfect complexes to bivariant operational $K$-theory. Comment: 46 pages, with an appendix by G. Vezzosi; v3: minor corrections, to appear in Algebra Number Theory |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.2140/ant.2021.15.341 |
| URL الوصول: | http://arxiv.org/abs/1907.00076 |
| رقم الأكسشن: | edsarx.1907.00076 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.2140/ant.2021.15.341 |
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