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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

2 votes
1 answer
289 views

Is the $\mathbb R$-split component of a torus defined over $\mathbb Q$ also defined over $\m...

Suppose $\mathbf T$ is an algebraic torus defined over $\mathbb Q$, it splits as $\mathbf T_s\cdot\mathbf T_a$, respectively split and anisotropic over $\mathbb R$. Are the subtori $\mathbf T_s$ and $ …
Jerry's user avatar
  • 511
12 votes
1 answer
668 views

Is every connected semisimple linear Lie group the connected component of (the real points o...

Is every connected semisimple linear Lie group the identity connected component of (the real points of) an algebraic group? I was told some fact along this line is true but could not find any ref …
Jerry's user avatar
  • 511