[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む79 (1002ﾚｽ)
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337(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/12/07(土)19:39 ID:H2e5WMAT(10/14) AAS
>>336

つづき

Completion of the proof
The deduction of the Riemann hypothesis from this estimate is mostly a fairly straightforward use of standard techniques and is done as follows.

Deligne's second proof
Deligne (1980) found and proved a generalization of the Weil conjectures, bounding the weights of the pushforward of a sheaf.
In practice it is this generalization rather than the original Weil conjectures that is mostly used in applications, such as the hard Lefschetz theorem. Much of the second proof is a rearrangement of the ideas of his first proof.
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338: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/12/07(土)19:39 ID:H2e5WMAT(11/14) AAS
>>337

つづき

外部ﾘﾝｸ:en.wikipedia.org
In mathematics, a Lefschetz pencil is a construction in algebraic geometry considered by Solomon Lefschetz, used to analyse the algebraic topology of an algebraic variety V.

It has been shown that Lefschetz pencils exist in characteristic zero. They apply in ways similar to, but more complicated than, Morse functions on smooth manifolds. It has also been shown that Lefschetz pencils exist in characteristic p for the etale topology.

Simon Donaldson has found a role for Lefschetz pencils in symplectic topology, leading to more recent research interest in them.
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