4 votes

Non-torsion points of Tate curves

What you are asking for does not exist, and there is no reason to expect it should. The set of all points of the Tate curve, or another elliptic curve, over a local field, or its algebraic closure, is ...
Will Sawin's user avatar
  • 135k
4 votes
Accepted

Isocrystal with no $F$-structure

The connection $D - \dfrac{a dx}{x}$ on the trivial line bundle on $\mathbb G_m$ has formal solutions proportional to $x^a$ which is convergent for $a \in \mathbb Z_p$. Hence the connection is ...
Will Sawin's user avatar
  • 135k
4 votes
Accepted

Equivalence between vector bundles with integrable connections to isocrystals

Let me briefly expand my comment into an answer. As Satan's Minion writes in the comments, this follows from (rigid) GAGA, but I think this fact is not entirely obvious. GAGA gives that ...
Daniel Litt's user avatar
  • 22.1k
2 votes

"General position" on $\mathbb{P}^1\times\mathbb{P}^1$

Five points are in a general position if pairs of points do not lie on the same ruling; quadruples of points do not lie on a conic. For six points you get an extra condition six points do not lie ...
Sasha's user avatar
  • 37k
1 vote

Frobenius action on the trivial connection

Since both connections are defined on the same domain, I managed to confuse myself with the definition of the pullback connection. The pullback connection extends via the Leibniz rule on a local base. ...
kindasorta's user avatar
  • 1,373

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