Keerthi Madapusi Pera

Department of Mathematics, SC 235,
Harvard University,
One Oxford St,
Cambridge, MA 02138, U.S.A.

Email: keerthi [at] math [dot] harvard [dot] edu

I just graduated from the the department of mathematics at the University of Chicago, and am now a Benjamin Peirce Fellow at Harvard. My advisor was Mark Kisin, who is now also at Harvard. I grew up in India and first came to the US to get a BS in mathematics at Yale. You can find my CV here.

I'm co-organizing the Number Theory Seminar here with Joe Rabinoff. Let one of us know if you would like to give a talk. You can find the schedule here.

Teaching:

I'm teaching Math 21b in Spring 2011.

Click here if you would like to do a Senior Thesis with me.

Research Interests:

• Integral models of Shimura varieties and their compactifications.
• Hodge cycles on abelian varieties.
• Integral p-adic Hodge theory.
• Logarithmic Dieudonne theory.

Thesis: Toroidal Compactifications of Integral Canonical Models of Shimura varieties of Hodge type (single spaced version).

Publications and pre-prints:

1. Toroidal compactifications of integral canonical models of Shimura varieties of Hodge type. Draft Abstract

   We construct smooth projective toroidal compactifications for the integral canonical models of Shimura varieties of Hodge type constructed by Kisin. This involves an interpretation of the complete local rings of Chai-Faltings compactifications of the moduli space of polarized abelian schemes as deformation rings of log 1-motifs. It also requires a new rationality statement for Hodge cycles on abelian varieties with respect to integral structures on cohomology obtained from Raynaud's $p$-adic analytic uniformizations. We then deduce the existence of an integral model for the Baily-Borel-Satake (or minimal) compactification, and show that it has the expected properties. We also prove most cases of Morita's conjecture on the everywhere potentially good reduction of abelian varieties whose Mumford-Tate groups are anisotropic modulo center.

2. Log $1$-motifs and log $F$-crystals, in preparation. Abstract

   This is a companion paper to 'Toroidal compactifications...'. The goal is to construct log crystalline realizations for families of degenerating abelian varieties. We use the language of log 1-motifs, which are logarithmic generalizations due to Kato of Deligne's 1-motifs. From this point of view, we are led to a natural proof of the p-adic comparison isomorphism for semi-stable abelian varieties, generalizing a proof of Faltings in the case of good reduction.

Some (very incomplete) notes of mine:

The first two were written back when I was an innocent first year student, who believed that the only way to learn something was to write it all up in gory detail. I still find parts of them useful, so I’ve put them up for general consumption. Caveat: citation in these notes is quite poor, but obviously stuff has made it into them from all over the place. And nothing in them is original (except maybe some of the organization).

· Basic Commutative Algebra

· Basic Algebraic Geometry

· Perfect complexes: The linear algebraic content of semi-continuity and base change

· Log p-divisible groups (after Kato)

Other news

You might have known me under the last name Madapusi Sampath (or simply Madapusi). I'm in the process of getting my name officially to Madapusi Pera, a combination of my last name and my wife's.