The Phenotype
  • Jeruzalem, Israël
  • Member for 3 years, 9 months
Stats
5,089
reputation
655k
reached
201
answers
3
questions
Loading…
About

I am actually a brainlet who likes to put bounties on random PDE questions that I see.

Location might not be correct.

Hodge conjecture: Let $X$ be a non-singular complex projective manifold. Then every Hodge class on $X$ is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of $X$.

Proof: Follows from Corollary 8.2.

$\downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow$

Corollary 8.2

Proof: Using Theorem 8.1, we can conclude that (...).

$\downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow$

Theorem 8.1

Proof: From lemma 7.6 we can see (...).

$\downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow$

Lemma 7.6

Proof: (...) and by Proposition 4.3 (...).

$\downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow$

Proposition 4.3

Proof: (...) and the last inequality is a direct consequence of Theorem 6 from (...) by Evans. See references.

$\downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow$

(...), Evans: Theorem 6

Proof: (...) "Without loss of generality" we may (...). "Obviously", (...). Assertion (ii) follows "similarly". (...) and "temporarily suppose" that (...). Now we will "reduce to the special case" as above (...). See Stein [SE, Chapter IV] for "the theory" of (...) and by Theorem 4 we have that (...).

$\downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow\ \ \ \ \ \downarrow$

(...), Evans: Theorem 4

Proof: The proof is trivial and left as an exercise to the reader (Problem 11).

Top network posts

We respect a laser-like focus on one topic.

9
gold badges
21
silver badges
34
bronze badges

Top tags (150)

Score 45
Posts 25
Posts % 12
Score 41
Posts 27
Score 37
Posts 22
Score 22
Posts 13
Score 21
Posts 10
Score 20
Posts 17

Top posts (204)

View all questions and answers