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97 questions
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2 votes
0 answers
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I am reading the preprint by Kramer-Miller and Upton on zeros of the Goss zeta function, and I am wondering why the Goss plane is defined the way it is. For $K$ a global function field of ...
Shyam R.'s user avatar
  • 121
1 vote
0 answers
53 views

let's suppose we have a function field $F$ and some Drinfeld modular variety of rank $r$ over $F$, with some level structure $Y^{(r)}(N)$. Then the field of constants of $Y^{(r)}(N)$ is some class ...
xir's user avatar
  • 2,281
2 votes
1 answer
164 views

Given a function field $K$ over $\Bbb C$ with a discrete valuation $v$, are there known criteria under which an automorphism of $K$ extends to the completion $K_v$? I’m aware of sufficient conditions ...
Anushka_Grace Chattopadhyay's user avatar
  • 139
5 votes
1 answer
236 views

Thanks for your help. I'm reading the paper Iwasawa main conjecture for the Carlitz cyclotomic extension and applications (https://arxiv.org/pdf/1412.5957). I find three questions about the motivation ...
Rellw's user avatar
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2 votes
0 answers
276 views

When I study Weil-étale cohomology put forward by S. Lichtenbaum in the paper The Weil-étale topology on schemes over finite fields, I find two questions. Let $X$ be a scheme of finite type over a ...
Rellw's user avatar
  • 473
2 votes
0 answers
221 views

Thanks for your help. I know the definition of Weil group and how to get it for $p$-adic local field cases. By reading the answer https://math.stackexchange.com/a/2898449/1007843, I write down my ...
Rellw's user avatar
  • 473
4 votes
1 answer
325 views

What is the minimal information needed to specify a Dirichlet character over the function field of a curve over a finite field? Over $ \mathbb{Q} $, a Dirichlet character is equivalent to a ...
Multramate's user avatar
  • 173
2 votes
0 answers
167 views

I am a beginner in research on Drinfeld modules. I have read the recent textbook by Papikian and am now starting to study Goss’s textbook and Anderson’s seminal paper on $t$-motives. However, I find ...
gualterio's user avatar
  • 1,153
7 votes
1 answer
697 views

In many papers on the function fields, it is commonly assumed that a curve is smooth, projective, and geometrically connected over a finite field. Could you please recommend the easiest (shortest) ...
gualterio's user avatar
  • 1,153
1 vote
0 answers
131 views

I'm following David Goss's book Basic structures of function field arithmetic. Let $L$ be an extension field of $L_0$ and $\sigma$ an automorphism of infinite order which fixes $L_0$. Let $L\{\sigma\}$...
MChocko's user avatar
  • 69
0 votes
1 answer
168 views

Let $p$ be an odd prime and $q$ a power of $p$. For a polynomial $f \in \mathbb{F}_q[T]$, let $\mu(f)$ be the Möbius function of $f$. For a positive integer $d$, let $M_d$ be the set of monic ...
user avatar
2 votes
0 answers
224 views

I'm studying Proposition 6.2.3 from Goss "Basic Structures of Function Field Arithmetic", page 184: Let $F$ be the sheaf of Data A (a torsion-free coherent $O_{\bar{X}}$-module on $\bar{X}$ ...
MChocko's user avatar
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2 votes
0 answers
168 views

I'm someone with more of a number fields background who recently started working on a project more in the function fields setting. I was reading Goss's book (Basic structures of function field ...
xir's user avatar
  • 2,281
3 votes
0 answers
90 views

Let $L$ and $K$ be isomorphic global fields (i.e. either function fields of curves over a finite field, or number fields). What is the complexity of finding an isomorphism between them? Is there a ...
Reyx_0's user avatar
  • 201
2 votes
0 answers
93 views

Over number fields, we have two natural degeneracy maps $$X_0(N)\leftarrow X_0(pN) \rightarrow X_0(N)$$ between the (compactified) moduli space of elliptic curves with level $pN$ and $N$ respectively (...
curious math guy's user avatar
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