“Frobenius splitting”的意思、由来-开放百科全书

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Frobenius splitting

释义

References
External links

In mathematics, a Frobenius splitting, introduced by {{harvs|txt|author1-link=Vikram Bhagvandas Mehta|last=Mehta|last2=Ramanthan|author2-link=Annamalai Ramanathan |year=1985}}, is a splitting of the injective morphism O_X→F_*O_X from a structure sheaf O_X of a characteristic p > 0 variety X to its image F_*O_X under the Frobenius endomorphism F_*.

{{harvtxt|Brion|Kumar|2005}} give a detailed discussion of Frobenius splittings.

A fundamental property of Frobenius-split projective schemes X is that the higher cohomology Hⁱ(X,L) (i > 0) of ample line bundles L vanishes.

References

{{Citation | last1=Brion | first1=Michel | last2=Kumar | first2=Shrawan | title=Frobenius splitting methods in geometry and representation theory | publisher=Birkhäuser Boston | location=Boston, MA | series=Progress in Mathematics | isbn=978-0-8176-4191-7 | doi=10.1007/b137486 | mr=2107324 | year=2005 | volume=231}}
{{Citation | last1=Mehta | first1=V. B. | last2=Ramanathan | first2=A. | title=Frobenius splitting and cohomology vanishing for Schubert varieties | doi=10.2307/1971368 | mr=799251 | year=1985 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=122 | issue=1 | pages=27–40}}

External links

Conference on Frobenius splitting in algebraic geometry, commutative algebra, and representation theory at Michigan, 2010.

1 : Algebraic geometry

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