skip to main content


Search for: All records

Creators/Authors contains: "Kedlaya, Kiran"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Abstract

    Using the formalism of Newton hyperplane arrangements, we resolve the open questions regarding angle rank left over from work of the first two authors with Roe and Vincent. As a consequence we end up generalizing theorems of Lenstra–Zarhin and Tankeev proving several new cases of the Tate conjecture for abelian varieties over finite fields. We also obtain an effective version of a recent theorem of Zarhin bounding the heights of coefficients in multiplicative relations among Frobenius eigenvalues.

     
    more » « less
  2. Let $X$ be a smooth scheme over a finite field of characteristic $p$.Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adicWeil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell\neq p$, and overconvergent $F$-isocrystals in rigid cohomology when $\ell=p$.Using the Langlands correspondence for global function fields in both the\'etale and crystalline settings (work of Lafforgue and Abe, respectively), onesees that on a curve, any coefficient object in one category has "companions"in the other categories with matching characteristic polynomials of Frobeniusat closed points. A similar statement is expected for general $X$; building onwork of Deligne, Drinfeld showed that any \'etale coefficient object has\'etale companions. We adapt Drinfeld's method to show that any crystallinecoefficient object has \'etale companions; this has been shown independently byAbe--Esnault. We also prove some auxiliary results relevant for theconstruction of crystalline companions of \'etale coefficient objects; thissubject will be pursued in a subsequent paper. 
    more » « less
  3. Abstract

    We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field$$\mathbb {F}_2$$F2and genus$$>1$$>1; and give a conjectural answer in the remaining cases. The conjecture will be resolved in subsequent papers.

     
    more » « less
  4. Anni, Samuele ; Karemaker, Valentijn ; Lorenzo García, Elisa (Ed.)
  5. Anni, Samuele ; Karemaker, Valentijn ; Lorenzo García, Elisa (Ed.)
  6. Abstract

    We show that for every integer$$m > 0$$m>0, there is an ordinary abelian variety over $${{\mathbb {F}}}_2$$F2that has exactlymrational points.

     
    more » « less