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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 …
YUAN Zhiri's user avatar
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 …
YUAN Zhiri's user avatar
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 …
YUAN Zhiri's user avatar