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

7 votes
0 answers
270 views

Complete curves in $\mathcal{M}_g$ all of whose Jacobians have trivial endomorpism ring

I'm trying to construct complete smooth curves $C$ in $\overline{M}_g$ such that for all points $S \in C \cap \mathcal{M}_g$, its Jacobian $\text{Jac}(S)$ satisfies $\text{End}(\text{Jac}(S)) = \mathb …
Gina's user avatar
  • 131
3 votes
2 answers
221 views

Reductive groups over arbitrary fields with disconnected relative root systems

Let $\mathbf{G}$ be a connected reductive group over a field $k$, not necessarily algebraically closed. Let $\Phi$ be the relative root system for $\mathbf{G}$ with respect to $k$, and assume that $\ …
Gina's user avatar
  • 131
3 votes

Reductive groups over arbitrary fields with disconnected relative root systems

After looking through the reference that Mikhail Borovoi gave me and tracing through a bunch of back-references, I found a fairly clear description of what holds in the following survey of Tits: Tits, …
Gina's user avatar
  • 131