Alex Youcis

Berkeley, CA

ayoucis.wordpress.com

Age: 24

I am a second year graduate student at the University of California, Berkeley.

My interests are generally in the field of arithmetic geometry. More specifically, I am interested in various aspects of the Langlands program. My advisor is Sug Woo Shin.

2d
comment What is the group structure on the ring of power series around a point that makes it "the completion of an elliptic curve" along that point?
The group law, which I do believe you're asking for (as part of your question), is relatively simple. Namely, since $E/k$ is a group scheme, you have a multiplication map $\mu:E\times_k E\to E$. This maps $(e,e)$ to $e$ (the identity element) and so gives you a map $\mathcal{O}_{E,e}\to \mathcal{O}_{E\times E,(e,e)}$. Passing to the completions, and using the fact that both are smooth, we get a map $k[[T]]\to k[[X,Y]]$. The image of $T$ is the formal group law associated to $E$.
Jul
27
awarded Enlightened
Jul
27
awarded Nice Answer
Jul
27
awarded Yearling
Jul
27
awarded Yearling
Jul
27
awarded Nice Question
Jul
26
awarded Commentator
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
@Niels Thanks for the reference!
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
Thanks for the nice explicit example Donu! By the way, you mentioned above that you thought that 2,3 were open. Do you still believe that? I haven't been able to find any explicit answers online, but that doesn't mean much. There is the book 'Fundamental Groups of Compact Kahler Manifolds', but I don't feel like reading hundreds of pages, and can't find a super relevant proposition. Thanks again!
Jul
26
comment Relationship between étale and topological $K(\pi,1)$s
I should've just looked in your thesis. :)
Jul
26
accepted Relationship between étale and topological $K(\pi,1)$s
Jul
25
revised Relationship between étale and topological $K(\pi,1)$s
added 3 characters in body
Jul
25
comment Relationship between étale and topological $K(\pi,1)$s
@potentiallydense I may be the potentially dense one. :) Thanks for pointing that out.
Jul
25
revised Relationship between étale and topological $K(\pi,1)$s
edited title
Jul
25
asked Relationship between étale and topological $K(\pi,1)$s
Jul
23
comment Difference between $K$-rational points and $K$-valued points
Containment of rings=field extension for fields. The terms are synonomous. And so yes, K-rational and K-points mean the same thing. :)
Jul
23
comment Neukirch's motivation for $p$-adic numbers
@Lubin I disagree in some sense. I think the analogy I mentioned above is pretty concrete. There is also this issue with regards to power series (albeit easier to fix). Abstractly $\widehat{\mathcal{O}_{X,x}}$ is a power series ring, and choosing an explicit isomorphism is choosing a center for the power series expansion. So, there are no unique coefficients, but 'natural ones', similarly to the case of p-adics.
Jul
22
comment Self-intersection number of fibered surface
I don't have it on hand, but if it's somewhere accessible, it'll be in chapter 9 of Qing Liu.
Jul
22
comment Weil: Fibre Spaces in Algebraic Geometry
Why don't you request it from a library? A few libraries near me have it. worldcat.org/title/fibre-spaces-in-algebraic-geometry/oclc/…
Jul
21
comment Continuity of Galois representations from cohomology
@dionysos It is for the finite pieces--the Z/l^nZ coeffs.
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