[過去ログ] Inter-universal geometry と ABC予想 24 (1002レス)
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338: 2018/02/05(月)21:54 ID:pf1Bs7WH(1/7) AAS
The main idea of the proof is, I think,
understood. We want to compute
the same thing in two different
ways. In particular, for (certain
elliptic) curves with at worst split
multiplicative reduction at certain
places (where you have Tate models and Tate parameters),
339: 2018/02/05(月)21:55 ID:pf1Bs7WH(2/7) AAS
we want to compute the valuation of
the tate parameters in two different
ways. One way is direct, and the
other way is indirect and uses
anabelian geometry. This is
interesting to us because of Szpiro's conjecture.
340: 2018/02/05(月)21:56 ID:pf1Bs7WH(3/7) AAS
The valuation of the tate parameter
is exactly the valuation of the
minimal discriminant of the elliptic
curve. This is the left hand side of
the Szpiro inequality an inequality
which is equivalent to the abc
conjecture. The second way is
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341: 2018/02/05(月)21:57 ID:pf1Bs7WH(4/7) AAS
In fact, we encode these vals in
terms of log vols which can be
reconstr(this is where these log-
shells come into play) and we can
only reconstr the region up to
monoid actions (these monoid
actions are the indet appearing in
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342: 2018/02/05(月)21:57 ID:pf1Bs7WH(5/7) AAS
The actual breakdown of what this
inequality means/is is what gives
rise to Theorem 1.10 in IUT4.
343: 2018/02/05(月)21:58 ID:pf1Bs7WH(6/7) AAS
The main technical aspects are
about the anabelian geometry that
go into the reconstruction. There
are many different versions of the
same objects introduced in the
paper which behave differently and
sorting all of this out in a clean way
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344: 2018/02/05(月)21:59 ID:pf1Bs7WH(7/7) AAS
Brian and Peter are mentioned a lot
but they honestly haven't done
anything in this. The names
Fucheng Tan and Emmanuel Lepage
are never mentioned but I think they
are two people (along with Chung
Pang) who I have learned the most
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