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.

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revised Direct image of vector bundle
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comment Direct image of vector bundle
@GeorgesElencwajg Good point. I think I conflated things in transcription from memory of the projection formula, and the $f_\ast$ coming from $f_\ast(\mathcal{E})$. Let me erase that for now, and I'll try and fix it later. Thanks!
2h
comment Direct image of vector bundle
@GeorgesElencwajg Hopefully I haven't made a mistake! This is just the projection formula on $\mathrm{CH}(X)_\mathbb{Q}$ and $\mathrm{ch}$ denotes the Chern character. Please let me know if I wrote nonsense!
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comment Direct image of vector bundle
@GeorgesElencwajg Hey Georges! Which formula are you referencing?
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revised Direct image of vector bundle
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answered Direct image of vector bundle
Feb
15
comment Applications of the Little and Great Theorems of Picard
Can you explain something to me Bruno? It seems as though what you're using is the Uniformization Theorem (the classification of simply connected Riemann surfaces). How does that follow from the big/small Picard theorems? The proof I know uses Green's functions/differential geometry.
Feb
13
answered What's With The Diagonal Morphism?
Feb
10
answered Examples of Non-Noetherian Valuation Rings
Feb
10
awarded Enlightened
Feb
10
awarded Nice Answer
Feb
4
revised Why do modular curves parametrise elliptic curves?
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Feb
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revised In what sense is $p$-adic Hodge theory related to ordinary (complex) Hodge theory?
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Feb
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revised Why do modular curves parametrise elliptic curves?
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Feb
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comment In what sense is $p$-adic Hodge theory related to ordinary (complex) Hodge theory?
@Joachim I fixed the $\mathbb{C}_K$/$G_K$ mix-ups I believe. Yes, when I write $g(\alpha)g(x)$, I mean that $g(\alpha)$ is the usual action of $g$ on $\mathbb{C}_K$, and $g(x)$ is the representation. Now, I probably put the statement 'terrible notation' at the wrong point. I didn't call it terrible because it was inconsistent, just that $\text{Rep}_F(G)$ should, at least in my opinion, only be for $F$-linear representations. Finally, yes, I mean the standard operations. So, $g(c\otimes x)=g(c)\otimes g(x)$ for $c\in\mathbb{C}_K$ and $x\in V$.
Feb
2
revised In what sense is $p$-adic Hodge theory related to ordinary (complex) Hodge theory?
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Feb
2
revised In what sense is $p$-adic Hodge theory related to ordinary (complex) Hodge theory?
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Feb
2
revised Why do modular curves parametrise elliptic curves?
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Feb
2
answered Why do modular curves parametrise elliptic curves?
Feb
2
revised In what sense is $p$-adic Hodge theory related to ordinary (complex) Hodge theory?
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