Grothendieck–Hirzebruch–Riemann–Roch theorem

Math Formula Information

Formula: ${\displaystyle {\mbox{ch}}(f_{\mbox{!}}{\mathcal {F}}^{\bullet }){\mbox{td}}(Y)=f_{*}({\mbox{ch}}({\mathcal {F}}^{\bullet }){\mbox{td}}(X))}$

Name: Grothendieck–Hirzebruch–Riemann–Roch theorem

Description:

Elements of the Formula

smooth quasiprojective scheme	${\displaystyle X}$	Geometric Object in algebraic geometry decribed by algebraic properties
smooth quasiprojective scheme	${\displaystyle Y}$	Geometric Object in algebraic geometry decribed by algebraic properties
proper morphism	${\displaystyle f}$	in algebraic geometry, an analogue of a proper map for algebraic varieties
Todd class	${\displaystyle \mathrm {td} }$	characteristic class in algebraic topology
Chern class	${\displaystyle \mathrm {ch} }$	characteristic classes on algebraic vector bundles
Push-forward (Chow groups)	${\displaystyle f_{*}}$	Map of Chow groups of the schemes induced by a morphism of schemes
Push-forward (Grothendieck groups)	${\displaystyle f_{!}}$	map of the Grothendieck groups induced by a map of schemes

Data Source

https://www.wikidata.org/wiki/Special:EntityPage/Q1899432