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School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
ELLIPTIC CURVES WITH MAXIMAL GALOIS ACTION ON THEIR TORSION POINTS
ELLIPTIC CURVES MAXIMAL GALOIS ACTION TORSION POINTS
2015/8/26
Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, ρE : Gal(k/k) → GL2(Z b). For a fixed number field k, we describe the ima...
ON THE SURJECTIVITY OF MOD REPRESENTATIONS ASSOCIATED TO ELLIPTIC CURVES
MOD REPRESENTATIONS ASSOCIATED ELLIPTIC CURVES
2015/8/26
Let E be an elliptic curve over the rationals that does not have complex multiplication. For each prime `, the action of the absolute Galois group on the `-torsion points of E can be given in terms of...
THE MODULI SPACE OF CURVES, DOUBLE HURWITZ NUMBERS, AND FABER’S INTERSECTION NUMBER CONJECTURE
DOUBLE HURWITZ NUMBERS FABER’S INTERSECTION NUMBER CONJECTURE
2015/7/14
We define the dimension 2g − 1 Faber-Hurwitz Chow/homology classes on the moduli
space of curves, parametrizing curves expressible as branched covers of P
1 with given ramification...
Caporaso and Harris derive recursive formulas counting nodal plane
curves of degree d and geometric genus g in the plane (through the appropriate number of xed
general points). We rephrase their ar...
ON THE MODULARITY OF ELLIPTIC CURVES OVER Q: WILD 3-ADIC EXERCISES.
Elliptic curve Galois representation modularity
2015/7/6
with c 0 mod N and d p mod N. The operators Tp for p6 jN can be simultaneously diagonalised on
the space Sk(N) and a simultaneous eigenvector is called an eigenform. If f is an eigenform then the...
The aim of this paper is to give a purely rigid-analytic development of the theory of canonical subgroups
with arbitrary torsion-level in generalized elliptic curves over rigid spaces over k (using L...
ERRATUM TO MODULAR CURVES AND RAMANUJAN’S CONTINUED FRACTION
q-series modular curve Ramanujan continued fraction
2015/7/6
This lemma is already false for k = p quite generally, and our error in the proof of the
lemma occurs in the line beginning “Evidently. . . ” (the formula given for (k, m+jk/p)
in that line is wrong...
Hierarchical Abstraction of Phase Response Curves of Synchronized Systems of Coupled Oscillators
Coupled Oscillators Response Curves Synchronized Systems
2011/7/6
We prove that a group of injection-locked oscillators, each
modelled using a nonlinear phase macromodel, responds as a single
oscillator to small external perturbations. More precisely, we show that...
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2010/12/28
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for t...
The rationality of the moduli spaces of trigonal curves of odd genus
trigonal curve rationality of moduli
2011/1/18
The moduli spaces of trigonal curves of odd genus g ≥ 5 are proven to be rational.
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2011/2/21
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail.
We study the inertia stack of [M_{0,n}/S_n], the quotient stack of the moduli stack of smooth genus 0 curves with n marked points via the action of the symmetric group S_n. Then we see how from this ...
Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation
elliptic curves the associative Yang-Baxter equation
2010/11/23
In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point $\tau$ from the upper half-plane and an invertible $n \tim...
Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve on...