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SUMMARY:Amadou Bah
DTSTART:20211216T130000Z
DTEND:20211216T140000Z
DTSTAMP:20260423T005816Z
UID:viasmag/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/viasmag/2/">
 Variation of the Swan conductor of an $\\mathbb{F}_{\\ell}$-sheaf on a rig
 id annulus</a>\nby Amadou Bah as part of VIASM Arithmetic Geometry Online 
 Seminar\n\n\nAbstract\nLet $C$ be a closed annulus of radii $r < r' \\in \
 \mathbb{Q}_{\\geq 0}$ over a complete discrete valuation field with algebr
 aically closed residue field of characteristic $p>0$. To an étale sheaf o
 f $\\mathbb{F}_{\\ell}$-modules $\\mathcal{F}$ on $C$\, ramified at most a
 t a finite set of rigid points of $C$\, one associates an Abbes-Saito Swan
  conductor function ${\\rm sw}_{\\mathcal{F}}: [r\, r']\\cap \\mathbb{Q}_{
 \\geq 0} \\to \\mathbb{Q}$ which\, for a radius $t$\, measures the ramific
 ation of $\\mathcal{F}_{\\lvert C^{[t]}}$ — the restriction of $\\mathca
 l{F}$ to the sub-annulus $C^{[t]}$ of $C$ of radius $t$ with $0$-thickness
  — along the special fiber of the normalized integral model of $C^{[t]}$
 . This function has the following remarkable properties: it is continuous\
 , convex and piecewise linear outside the radii of the ramification points
  of $\\mathcal{F}$\, with finitely many integer slopes whose variation bet
 ween radii $t$ and $t'$ can be expressed as the difference of the orders o
 f the characteristic cycles of $\\mathcal{F}$ at $t$ and $t'$. In this tal
 k\, I will explain the construction of ${\\rm sw}_{\\mathcal{F}}$ and the 
 key nearby cycles formula in establishing the aforementioned properties of
  ${\\rm sw}_{\\mathcal{F}}$.\n
LOCATION:https://researchseminars.org/talk/viasmag/2/
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