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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
3
votes
1
answer
153
views
A rationality problem about $F$-points in tori
Let $F$ be a finite field, and $T$ be a torus over $F$. Assume that $T_1,T_2$ are two $F$-subtori of $T$, such that $T_1 \times T_2 \to T,(t_1,t_2) \mapsto t_1 t_2$ is surjective with finite kernel $K …
16
votes
1
answer
2k
views
Relation between Weil Conjecture and Langlands Program
Recently I read Gelbart's An Elementary Introduction To The Langlands Program, which explained the origin of the program, and this question came to me. For an elliptic curve over finite field, the ass …
7
votes
2
answers
1k
views
About Abhyankar's conjecture
I just came to this conjecture (proved by M.Raynaud and D.Harbater in 1994) last weekend, in Fresnel and v.d.Put's book Rigid Geometry and Its Applications. It claims that all quasi $p$-group $G$ coul …