Homepage of  Tanya Kaushal Srivastava

IST Postdoctoral Fellow
Hausel’s group
IST Austria.

 


Teaching

I am teaching a course on Moduli Space of Curves in Spring 2020 and you will find the details here

I took a (virtual) Quiz as a final exam for the course, you can find the details and quiz slides here

Current Seminars


Publications and Notes

Preprints

  • Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences (Preprint pdf)

I show that for Abelian Varieties, every automorphism lifts as a morphism if and only if it lifts as a derived autoequivalence to a characteristic zero lift. But even for the case of elliptic curves, there are more ways to lift an automorphism as an autoequivalence than just as a morphism, although in this case the autoequivalence we get are just twist of the lift of automorphism with the lift of the structure sheaf of the graph of the automorphism. 

In preparation

  • Fully Faithfulness Criterion for Functors of (Twisted) Derived Categories, joint with Katrina Honigs 

We give another proof for the Caldararu’s criterion of checking when a twisted Fourier-Mukai functor gives an equivalence and we are working on extending a modified version of this criterion to positive characteristic and even more generally to the setting of smooth proper Deligne Mumford stacks in positive characteristic, the coarse moduli space of such stacks can have at worst quotient singularities, which being in positive characteristic need not be even Cohen Macaulay, unlike in the case of characteristic zero.

  • Counting Twisted Derived Equivalent Ordinary K3 Surfaces, joint with Sofia Tirabassi and Piotr Achinger.

We show that every Brauer class over an ordinary K3 surface has a preferred lift to the canonical lift of the underlying K3 surface and then we are working on a theory of moduli space of twisted K3 surfaces in characteristic p to be able to count the number of twisted derived Fourier-Mukai partner of an ordinary K3 surface.

 



Past seminars:

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Past Conferences and Summer/Winter Schools (Participation/Talks)