Imperial College London

DrAmbrusPal

Faculty of Natural SciencesDepartment of Mathematics

Senior Lecturer
 
 
 
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Contact

 

+44 (0)20 7594 8479a.pal

 
 
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Location

 

Huxley 663Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

28 results found

Lazda C, Pal A, 2019, Cycle classes in overconvergent rigid cohomology and a semistable Lefschetz (1,1) theorem, Compositio Mathematica, Vol: 155, Pages: 1025-1045, ISSN: 0010-437X

In this article we prove a semistable version of the variational Tate conjecture for divisors in crystalline cohomology, stating that a rational (logarithmic) line bundle on the special fibre of a semistable scheme over kJtK lifts to the total space if and only if its first Chern class does. The proof is elementary, using standard properties of the logarithmic de Rham–Witt complex. As a corollary, we deduce similar algebraicity lifting results for cohomology classes on varieties over global function fields. Finally, we give a counter-example to show that the variational Tate conjecture for divisors cannot hold with Qp-coefficients.

Journal article

Pal A, Endre S, 2018, The fibration method over real function fields

Let R(C) be the function field of a smooth, irreducible projective curve over R. Let X be a smooth, projective, geometrically irreducible variety equipped with a dominant morphism f onto a smooth projective rational variety with a smooth generic fibre over R(C). Assume that the cohomological obstruction introduced by Colliot-Thélène is the only one to the local-global principle for rational points for the smooth fibres of f over R(C)-valued points. Then we show that the same holds for X, too, by adopting the fibration method similarly to Harpaz--Wittenberg. We also show that the strong vanishing conjecture for n-fold Massey products holds for fields of virtual cohomological dimension at most 1 using a theorem of Haran.

Working paper

Krishnamoorthy R, Pal A, 2018, Rank 2 local systems and abelian varieties

LetX/Fqbe a smooth geometrically connected variety. Inspired by work of Corlette-Simpson overC, we formulate a conjecture that absolutely irreducible rank 2 local systems withinfinite monodromy onX“come from families of abelian varieties”. WhenXis a projective variety,we prove that ap-adic variant of this conjecture reduces to the case of projective curves. If oneassumes a strong form of Deligne’s (p-adic)companions conjecturefrom Weil II, this implies that thel-adic version of our conjecture for projective varieties also reduces to the case of projective curves.Along the way we prove Lefschetz theorems for homomorphismsof abelian schemes and Barsotti-Tategroups. We also answer affirmitavely a question of Grothendieck on extending abelian schemes viatheirp-divisible groups.

Working paper

Pal A, 2018, Iterated line integrals over Laurent series fields of characteristic p, Publications mathématiques de Besançon, Vol: 2017, Pages: 109-126

Journal article

Munao S, El-Guindy A, Pal A, Pellarin Fet al., 2017, Obituary of David Goss In Memoriam, JOURNAL OF NUMBER THEORY, Vol: 179, Pages: 1-2, ISSN: 0022-314X

Journal article

Pal A, Schlank TM, 2017, The Brauer-Manin obstruction to the local-global principle for the embedding problem, Publisher: arXiv

We study an analogue of the Brauer-Manin obstruction to the local-global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the (algebraic) Brauer-Manin obstruction is the only one to weak approximation when the embedding problem has abelian kernel. As a part of our investigations we also give a new, elegant description of the Tate duality pairing and prove a new theorem on the cup product.

Working paper

Lazda C, Pal A, 2017, A homotopy exact sequence for overconvergent isocrystals

n this article we prove exactness of the homotopy sequenceof overconvergentp-adic fundamentalgroups for a smooth and projective morphism in characteristicp. We do so by first proving a correspondingresult for rigid analytic varieties in characteristic 0, following dos Santos [dS15] in the algebraic case. Incharacteristicp, we then proceed by a series of reductions to the case of a liftable family of curves, where wecan apply the rigid analytic result.

Working paper

Lazda C, Pál A, 2016, Rigid cohomology over Laurent series fields, Publisher: Springer, ISBN: 9783319309514

Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic.

Book

Colliot-Thelene JL, Pal A, Skorobogatov AN, 2016, Pathologies of the Brauer-Manin obstruction, Mathematische Zeitschrift, Vol: 282, Pages: 799-817, ISSN: 1432-1823

Journal article

Pal A, 2015, The $p$-adic monodromy group of abelian varieties over global function fields of characteristic $p$, Publisher: arXiv

We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonné modules of abelian varieties defined over global function fields of characteristic p. As a corollary we deduce that monodromy groups of such overconvergent crystalline Dieudonné modules are reductive, and after a finite base change of coefficients their connected components are the same as the connected components of monodromy groups of Galois representations on the corresponding l-adic Tate modules, for l different from p. We also show such a result for general compatible systems incorporating overconvergent F-isocrystals, conditional on a result of Abe.

Working paper

Pal A, 2015, Etale homotopy equivalence of rational points on algebraic varieties, ALGEBRA & NUMBER THEORY, Vol: 9, Pages: 815-873, ISSN: 1937-0652

Journal article

Pal A, 2014, On the Chow groups of certain geometrically rational 5-folds, JOURNAL OF NUMBER THEORY, Vol: 139, Pages: 53-79, ISSN: 0022-314X

Journal article

Pal A, 2014, Hodge theory and the Mordell-Weil rank of elliptic curves over extensions of function fields, JOURNAL OF NUMBER THEORY, Vol: 137, Pages: 166-178, ISSN: 0022-314X

Journal article

Pal A, 2014, ON THE NILPOTENT SECTION CONJECTURE FOR FINITE GROUP ACTIONS ON CURVES, MATHEMATIKA, Vol: 60, Pages: 183-200, ISSN: 0025-5793

Journal article

Pal A, 2013, SOLVABLE POINTS ON GENUS-ONE CURVES OVER LOCAL FIELDS, JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, Vol: 12, Pages: 31-42, ISSN: 1474-7480

Journal article

Pal A, 2013, Curves which do not Become Semi-Stable After any Solvable Extension, RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, Vol: 129, Pages: 265-276, ISSN: 0041-8994

Journal article

Karolyi G, Pal A, 2012, The cyclomatic number of connected graphs without solvable orbits, JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, Vol: 27, Pages: 213-240, ISSN: 0970-1249

Journal article

Pal A, 2011, The real section conjecture and Smith's fixed-point theorem for pro-spaces, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, Vol: 83, Pages: 353-367, ISSN: 0024-6107

Journal article

Pal A, 2010, A Rigid Analytical Regulator for the K-2 of Mumford Curves, PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, Vol: 46, Pages: 219-253, ISSN: 0034-5318

Journal article

Pal A, 2010, On the Kernel and the Image of the Rigid Analytic Regulator in Positive Characteristic, PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, Vol: 46, Pages: 255-288, ISSN: 0034-5318

Journal article

Pal A, 2010, The Rigid Analytical Regulator and K-2 of Drinfeld Modular Curves, PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, Vol: 46, Pages: 289-334, ISSN: 0034-5318

Journal article

Pal A, 2010, On the torsion of Drinfeld modules of rank two, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, Vol: 640, Pages: 1-45, ISSN: 0075-4102

Journal article

Pal A, 2010, The Manin constant of elliptic curves over function fields, ALGEBRA & NUMBER THEORY, Vol: 4, Pages: 509-545, ISSN: 1937-0652

Journal article

Ambrus Pal, 2007, On the Eisenstein ideal of Drinfeld modular curves, International Journal of Number Theory

Journal article

Pal A, 2006, Proof of an exceptional zero conjecture forelliptic curves over function fields, Mathematische Zeitschrift, Vol: 254, Pages: 461-483, ISSN: 0025-5874

Journal article

Pal A, 2005, On the torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves, Documenta Math., Vol: 10, Pages: 131-198, ISSN: 1431-0643

Journal article

Pal A, 2004, Solvable points on projective algebraic curves, Canad. J. Math., Vol: 56, Pages: 612-637, ISSN: 0008-414X

Journal article

Pal A, 2004, Theta series, Eisenstein series and Poincareseries over function fields, Canad. J. Math., Vol: 56, Pages: 406-430, ISSN: 0008-414X

Journal article

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