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DTSTART;TZID=Europe/Berlin:20261029T141500
DTEND;TZID=Europe/Berlin:20261029T151500
DTSTAMP:20261023T090601Z
CREATED:20260730T100545Z
LAST-MODIFIED:20261023T090601Z
UID:13883-1793283300-1793286900@crc326gaus.de
SUMMARY:AGTZ Kolloquium
DESCRIPTION:Matteo Montagnani (Mainz) \nGeometric properties of analytic categories of sheaves \nIn algebraic geometry\, it is a well-established practice to study geometric properties of algebraic varieties through the study of certain categories of sheaves. For instance\, smooth algebraic varieties can be intrinsically characterized using Kontsevich’s notion of a smooth category. In this talk\, we discuss the key obstacles to adapting this categorical perspective to analytic geometry\, where classical sheaf-theoretic and tensor-product operations are not well-behaved. We then show how the framework of condensed mathematics\, introduced by Clausen and Scholze\, can be used to categorically characterize geometric properties of (rigid) analytic spaces.
URL:https://crc326gaus.de/event/agtz-kolloquium-11/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Georg Tamme":MAILTO:georg.tamme@uni-mainz.de
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DTSTART;TZID=Europe/Berlin:20261029T160000
DTEND;TZID=Europe/Berlin:20261029T180000
DTSTAMP:20261022T142949Z
CREATED:20261022T142449Z
LAST-MODIFIED:20261022T142949Z
UID:14693-1793289600-1793296800@crc326gaus.de
SUMMARY:Oberseminar Algebra und Geometrie
DESCRIPTION:Amine Koubaa (Leibniz Universität Hannover): Beauville Laszlo theorems for discretely ringed adic spaces \nAbstract: Let $(A\,A^+)$ be a discretely ringed Huber pair\, and let $f\in A$ be a non-zero divisor. Under mild conditions\, Bhatt proves the existence of an equivalence of $\infty$-categories \n\[\nD(A)\cong D(\hat{A}_f)\times_{D(\hat{A}_f[1/f])} D(A[1/f])\,\n\]\nwhich restricts to an equivalence of Categories\, originally proven by Beauville and Laszlo\,\n\[\n\textrm{Mod}(A)\cong \textrm{Mod}(\hat{A}_f)\times_{\textrm{Mod}(\hat{A}_f[1/f])} \textrm{Mod}(A[1/f]).\n\]\nTo remedy the absence of a category of quasi-coherent sheaves on discretely ringed adic space\, we prove a similar equivalence on the derived category of solid modules over analytic rings\, introduced by Clausen and Scholze\n\[\nD((A\,A^+)_\solid)\cong D((\hat{A}_f\,\hat{A}_f^+)_\solid)\times_{D((\hat{A}_f[1/f]\,\hat{A}_f^+[1/f])_\solid)} D((A[1/f]\,A^+[1/f])_\solid).\n\]\nWe conjecture a similar result holds for a category of “analytically coherent $\mathcal{O}^+$ modules” denoted by $\mathcal{C}^+(X)$ on a discretely ringed adic space $X$: We prove the result when $A=A^+$ is a dvr and $f$ is a uniformizer.
URL:https://crc326gaus.de/event/oberseminar-algebra-und-geometrie-13/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 309
CATEGORIES:GAUS-Seminar
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20261030T133000
DTEND;TZID=Europe/Berlin:20261030T143000
DTSTAMP:20261023T084510Z
CREATED:20261021T121253Z
LAST-MODIFIED:20261023T084510Z
UID:14677-1793367000-1793370600@crc326gaus.de
SUMMARY:Local-global compatibility at p of automorphic Galois representations over CM fields
DESCRIPTION:Dmitri Whitmore (University of Cambridge) \nAbstract:\nThe Langlands programme predicts a correspondence between automorphic forms and Galois representations. A key expectation is local-global compatibility\, which relates this global correspondence to the local Langlands correspondence. For regular algebraic cuspidal automorphic representations over CM fields\, associated p-adic Galois representations have been constructed\, but establishing this compatibility at primes above p has remained an important open problem. \nIn this talk\, I will discuss joint work with Lambert A’Campo\, Bence Hevesi\, and Jack Thorne establishing local-global compatibility at p up to semisimplification. As a consequence\, the associated Galois representations are geometric. I will discuss applications to new cases of the adjoint Bloch–Kato Selmer vanishing conjecture and outline how we remove the hypotheses on the mod p Galois representations required by previous approaches to local-global compatibility.
URL:https://crc326gaus.de/event/tba-152/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
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DTSTART;TZID=Europe/Berlin:20261030T153000
DTEND;TZID=Europe/Berlin:20261030T170000
DTSTAMP:20261026T100831Z
CREATED:20260917T123745Z
LAST-MODIFIED:20261026T100831Z
UID:14130-1793374200-1793379600@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Chirantan Chowhury (TU Darmstadt): Fundamental groups of proper algebraic stacks are finitely presented \nThe question of topological finite presentation of etale fundamental groups for proper schemes over algebraically closed fields of positive characteristic\, raised by Grothendieck\, remained open until recently. It was resolved for smooth projective varieties by Esnault\, Shusterman and Srinivas. Lara\, Srinivas and Stix have extended this result to connected proper schemes. In this talk\, I present my joint work with Ludvig Modin\, in which we extend this result to algebraic stacks. In particular\, we show that for connected proper algebraic stacks with finite inertia over an algebraically closed field\, the etale fundamental group\, as introduced by Noohi\, is topologically finitely presented. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl)
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-42/
LOCATION:Darmstadt\, Room 401 and Zoom\, Schlossgartenstraße 7\, Darmstadt\, 64289\, Germany
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Sabrina Pauli":MAILTO:pauli@mathematik.tu-darmstadt.de
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