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Results tagged with characteristic-p
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user 121
Fields of characteristic $p$, i.e., fields for which there is a prime $p$ such that $px=0$ for each $x$. Do not use this tag for questions on characteristic polynomials of a matrix.
63
votes
Accepted
Is there a high-concept explanation for why characteristic 2 is special?
I think there are two phenomena at work, and often one can separate behaviors based on whether they are "caused by''one or the other (or both). One phenomenon is the smallness of $2$, i.e., the expres …
- 45.7k
37
votes
3
answers
5k
views
Is there a nice proof of the fact that there are (p-1)/24 supersingular elliptic curves in c...
If $k$ is a characteristic $p$ field containing a subfield with $p^2$ elements (e.g., an algebraic closure of $\mathbb{F}_p$), then the number of isomorphism classes of supersingular elliptic curves o …
- 45.7k
22
votes
What does "supersingular" mean?
There are many equivalent ways to define supersingularity for an elliptic curve over a characteristic $p$ field. One of them is that the $p$-torsion of the curve is connected, i.e., it is a purely in …
- 45.7k
16
votes
2
answers
1k
views
Is the tangent space functor from PD formal groups to Lie algebras an equivalence?
The previous version of this question was rather badly broken, and I hope this version makes some sense.
There have been a few questions on MathOverflow about how much representation-theoretic inform …
- 45.7k
14
votes
Intuitive pictures in characteristic p
I heard the following analogy when talking to some specialists in absolute de Rham theory. I think Deninger's name was mentioned at about the same time.
One possible way to imagine a variety over $\ …
- 45.7k
11
votes
Is there a nice proof of the fact that there are (p-1)/24 supersingular elliptic curves in c...
This will be a summary of the proof referenced by BCnrd in the comments, for the benefit of those that haven't looked through Katz, Mazur, Arithmetic Moduli of Elliptic Curves. A scan is available as …
10
votes
Is the Characteristic of a Field Detectable from the Topology of a Topological Vector Space?
Torsten Ekedahl answered your first question in a nontrivial set of cases. As a concrete example, the characteristic two field $\mathbb{F}_2((t))$ is homeomorphic to the characteristic zero field $\m …
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9
votes
current status of crystalline cohomology?
Kedlaya gave a talk in August in which he mentioned some work of Daniel Caro on finiteness for rigid cohomology with coefficients (some of which is on the ArXiv). On the same page, you can find notes …
- 45.7k
8
votes
Algebraically closed fields of positive characteristic
The spherical completion (aka maximal completion) of $\overline{\mathbb{F}_p((t))}$ is an example of an algebraically closed field of characteristic p that hasn't been mentioned here yet. The "spheri …
- 45.7k
7
votes
Ways to characterize supersingular primes?
Supersingular primes are those primes p for which all supersingular elliptic curves over an algebraic closure of Fp have j-invariant in Fp. There is a theorem of Deuring that implies the j-invariant …
- 45.7k
2
votes
Finite extension of fields with no primitive element
If you're willing to work with commutative rings instead of just fields, you can gain some Galois-theoretic insight by base-changing to an algebraic closure $\bar{K}$ (or even a suitably large finite …
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