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 Sep30 awarded Explainer Sep20 awarded Yearling Sep6 awarded Nice Answer Jul2 awarded Curious May25 comment Frobenius action on $\overline{\mathbb Q_p}$ @JyrkiLahtonen The Frobenius is never an automorphism in characteristic 0, so that proof doesn't apply. The map still makes sense in many situations. The question only claims that it is an automorphism of $\mathbb{F}_p$. May21 comment Étale cohomology and Picard group of curves Do you want $X$ to be defined over $\overline{\mathbb{Q}}$ or $\mathbb{Q}$? May11 comment Is Calculus a requirement for Better Statistics? I'd strongly disagree with the "data science" person part. Most of a data scientists job is to build the models. You absolutely cannot build a good model without knowing the inner workings of the techniques. I don't know what pure statisticians do in the real world, but I would also imagine they build models too. Apr28 revised An isogeny of elliptic curves induces a $\mathbb{Z}_l$-linear map incorporated a comment into the answer Apr26 answered An isogeny of elliptic curves induces a $\mathbb{Z}_l$-linear map Apr25 comment Find the maximal $p$-divisible subgroup of $(\mathbb{Q},+)$ and $(\mathbb{Q}^{\times},\cdot)$? It is possible that a group $G$ has no maximal subgroup, but there is a maximal subgroup satisfying an additional property. For example, suppose there was only one proper subgroup with that property. Apr24 comment What is ${\rm cov}(e_i, \hat y_i)$ in simple linear regression? Cross-posted: stats.stackexchange.com/questions/94967/… Apr23 comment Frobenius on projective variety is not an isomorphism? Notice that when you have a morphism explicitly given in coordinates you can compute the Jacobian to see what the induced map on tangent spaces is. In this case it is the zero map because of the characteristic! An isomorphism must induce an isomorphism on tangent spaces as well. In other words, the Frobenius morphism is singular everywhere. Apr22 comment Why doesn't SAGE understand reduced expressions mod p in a finite field extension? Also, I think for GF(p) you are fine just assuming that it stores the representative classes as integers, but in general I would write GF(p^n, repr='int') to force the representatives to be integers. Apr22 comment Prove that $r^n/n!$ converges where $n\ge r$ I think there is a typo. What does $n\geq r$ have to do with anything? Aren't you proving something where $n\to \infty$? Apr20 comment What should one do if one works on a problem and submits a paper only to find that it is already in some book? Is it the exact same proof? I know of tons of published papers called things like "A New Proof of ... " Apr19 comment Computing the genus in positive characteristic It seems likely that you won't be able to "rule out" wild ramification ... because depending on the degree $d$ there will be cases where you do have wild ramification. I remember doing this problem a few years ago and found it fun and enlightening. I'll play around with it later today to see if I remember how it goes. Apr12 comment Is (the proof of) Fermat's last theorem completely, utterly, totally accepted like $3+4=7$? @DonAntonio I think maybe you are underestimating the amount of math research done every year. The Math Reviews (which only reviews actual published stuff!!) puts up about 86,000 publications per year. I assure you most of that is vetted by far less than 100 people. In the context of the question, one would never write "if this result is true" of those published papers read by maybe one other person, and hence one would definitely not write that for FLT which has been vetted much more thoroughly. Apr12 comment Is (the proof of) Fermat's last theorem completely, utterly, totally accepted like $3+4=7$? @DonAntonio Suppose only 100 people really understand it. Wouldn't you agree that 100 people is way more than most proofs that come out? Most theorems are fairly insignificant and the person that wrote it plus maybe a referee plus maybe 1 or 2 other people read them. The prominence and significance of FLT makes it much more widely read and understood than most other theorems proved in the last 50 years (also the Taylor-Wiles part is pretty "basic" stuff by today's standards, I'm not referring to the full modularity theorem). Apr12 comment Is (the proof of) Fermat's last theorem completely, utterly, totally accepted like $3+4=7$? I think there is such a thing as degree of belief in a proof, because there could always be some unnoticed mistake (this has happened throughout history). In the case of FLT, this has actually been checked and understood by such a vast number of people in comparison to most proofs that I'd have as much confidence in it as something like the Fundamental Theorem of Calculus. I would definitely not make that type of caveat which would probably be perceived as quite insulting to those that have checked the proof. Apr11 awarded Notable Question